x=3x^2-7x-2

Solution for x=3x^2-7x-2 equation:

x=3x^2-7x-2

We move all terms to the left:

x-(3x^2-7x-2)=0

We get rid of parentheses

-3x^2+x+7x+2=0

We add all the numbers together, and all the variables

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

a = -3; b = 8; c = +2;
Δ = b2-4ac
Δ = 82-4·(-3)·2
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{22}}{2*-3}=\frac{-8-2\sqrt{22}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{22}}{2*-3}=\frac{-8+2\sqrt{22}}{-6}
$