Answer:
The solution to the quadratic equation be:
Step-by-step explanation:
Given the expression
3x² – 2x = 5
Solving with the quadratic formula
![3x^2-2x=5](https://tex.z-dn.net/?f=3x%5E2-2x%3D5)
subtract 5 from both sides
![3x^2-2x-5=5-5](https://tex.z-dn.net/?f=3x%5E2-2x-5%3D5-5)
Simplify
![3x^2-2x-5=0](https://tex.z-dn.net/?f=3x%5E2-2x-5%3D0)
For a quadratic equation of the form ax²+bx+c=0
![x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x_%7B1%2C%5C%3A2%7D%3D%5Cfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
For a = 3, b = -2, c = -5
![x_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:3\left(-5\right)}}{2\cdot \:3}](https://tex.z-dn.net/?f=x_%7B1%2C%5C%3A2%7D%3D%5Cfrac%7B-%5Cleft%28-2%5Cright%29%5Cpm%20%5Csqrt%7B%5Cleft%28-2%5Cright%29%5E2-4%5Ccdot%20%5C%3A3%5Cleft%28-5%5Cright%29%7D%7D%7B2%5Ccdot%20%5C%3A3%7D)
![x_{1,\:2}=\frac{-\left(-2\right)\pm \:8}{2\cdot \:3}](https://tex.z-dn.net/?f=x_%7B1%2C%5C%3A2%7D%3D%5Cfrac%7B-%5Cleft%28-2%5Cright%29%5Cpm%20%5C%3A8%7D%7B2%5Ccdot%20%5C%3A3%7D)
Separate the solutions
![x_1=\frac{-\left(-2\right)+8}{2\cdot \:3},\:x_2=\frac{-\left(-2\right)-8}{2\cdot \:3}](https://tex.z-dn.net/?f=x_1%3D%5Cfrac%7B-%5Cleft%28-2%5Cright%29%2B8%7D%7B2%5Ccdot%20%5C%3A3%7D%2C%5C%3Ax_2%3D%5Cfrac%7B-%5Cleft%28-2%5Cright%29-8%7D%7B2%5Ccdot%20%5C%3A3%7D)
solving
![x_1=\frac{-\left(-2\right)+8}{2\cdot \:3}](https://tex.z-dn.net/?f=x_1%3D%5Cfrac%7B-%5Cleft%28-2%5Cright%29%2B8%7D%7B2%5Ccdot%20%5C%3A3%7D)
![=\frac{2+8}{2\cdot \:3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B2%2B8%7D%7B2%5Ccdot%20%5C%3A3%7D)
![=\frac{10}{6}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B10%7D%7B6%7D)
![=\frac{5}{3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B5%7D%7B3%7D)
also solving
![x_2=\frac{-\left(-2\right)-8}{2\cdot \:3}](https://tex.z-dn.net/?f=x_2%3D%5Cfrac%7B-%5Cleft%28-2%5Cright%29-8%7D%7B2%5Ccdot%20%5C%3A3%7D)
![=\frac{2-8}{2\cdot \:3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B2-8%7D%7B2%5Ccdot%20%5C%3A3%7D)
![=\frac{-6}{2\cdot \:3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-6%7D%7B2%5Ccdot%20%5C%3A3%7D)
![=\frac{-6}{6}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-6%7D%7B6%7D)
![=-\frac{6}{6}](https://tex.z-dn.net/?f=%3D-%5Cfrac%7B6%7D%7B6%7D)
![=-1](https://tex.z-dn.net/?f=%3D-1)
Therefore, the solution to the quadratic equation be: