Question

6. 3x2 – 2x = 5 Quadratic formula

Answer 1

Answer:

The solution to the quadratic equation be:

$x=\frac{5}{3},\:x=-1$  

Step-by-step explanation:

Given the expression

3x² – 2x = 5

Solving with the quadratic formula

$3x^2-2x=5$

subtract 5 from both sides

$3x^2-2x-5=5-5$

Simplify

$3x^2-2x-5=0$

For a quadratic equation of the form ax²+bx+c=0

$x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

For a = 3, b = -2, c = -5

$x_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:3\left(-5\right)}}{2\cdot \:3}$

$x_{1,\:2}=\frac{-\left(-2\right)\pm \:8}{2\cdot \:3}$

Separate the solutions

$x_1=\frac{-\left(-2\right)+8}{2\cdot \:3},\:x_2=\frac{-\left(-2\right)-8}{2\cdot \:3}$

solving

$x_1=\frac{-\left(-2\right)+8}{2\cdot \:3}$

    $=\frac{2+8}{2\cdot \:3}$

    $=\frac{10}{6}$

    $=\frac{5}{3}$

also solving

$x_2=\frac{-\left(-2\right)-8}{2\cdot \:3}$

    $=\frac{2-8}{2\cdot \:3}$

    $=\frac{-6}{2\cdot \:3}$

    $=\frac{-6}{6}$

     $=-\frac{6}{6}$

     $=-1$

Therefore, the solution to the quadratic equation be:

$x=\frac{5}{3},\:x=-1$