3(x=2)2+2x2=3x-8

Solution for 3(x=2)2+2x2=3x-8 equation:

3(x=2)2+2x^2=3x-8

We move all terms to the left:

3(x-(2)2+2x^2)=0

We multiply parentheses

6x^2+3x-66=0

a = 6; b = 3; c = -66;
Δ = b2-4ac
Δ = 32-4·6·(-66)
Δ = 1593
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1593}=\sqrt{9*177}=\sqrt{9}*\sqrt{177}=3\sqrt{177}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{177}}{2*6}=\frac{-3-3\sqrt{177}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{177}}{2*6}=\frac{-3+3\sqrt{177}}{12}
$