x=3x^2+2x-8

Solution for x=3x^2+2x-8 equation:

x=3x^2+2x-8

We move all terms to the left:

x-(3x^2+2x-8)=0

We get rid of parentheses

-3x^2+x-2x+8=0

We add all the numbers together, and all the variables

-3x^2-1x+8=0

a = -3; b = -1; c = +8;
Δ = b2-4ac
Δ = -12-4·(-3)·8
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{97}}{2*-3}=\frac{1-\sqrt{97}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{97}}{2*-3}=\frac{1+\sqrt{97}}{-6}
$