Question

Use the quadratic formula to si 3x2 + 8x – 4= 0

Answer 1

Answer:

$\large\boxed{x=\dfrac{-4-2\sqrt7}{3}\ or\ x=\dfrac{-4+2\sqrt7}{3}}$

Step-by-step explanation:

$\text{The quadratic formula for a quadratic equation}\ ax^2+bx+c=0\\\\\text{determinant:}\ \Delta=b^2-4ac\\\\\text{If}\ \Delta0,\ \text{then the equation has two different solutions}\ x=\dfrac{-b\pm\sqrt\Delta}{2a}.$

$\text{We have:}\\\\3x^2+8x-4=0\\\\a=3,\ b=8,\ c=-4\\\\\Delta=8^2-4(3)(-4)=64+48=112>0\\\sqrt\Delta=\sqrt{112}=\sqrt{(16)(7)}=\sqrt{16}\cdot\sqrt7=4\sqrt7\\\\x=\dfrac{-8\pm4\sqrt7}{2(3)}=\dfrac{-8\pm4\sqrt7}{6}=\dfrac{2(-4\pm2\sqrt7)}{6}=\dfrac{-4\pm2\sqrt7}{3}$