X=2x^2-3x-2

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

X=2X^2-3X-2

We move all terms to the left:

X-(2X^2-3X-2)=0

We get rid of parentheses

-2X^2+X+3X+2=0

We add all the numbers together, and all the variables

-2X^2+4X+2=0

a = -2; b = 4; c = +2;
Δ = b2-4ac
Δ = 42-4·(-2)·2
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{2}}{2*-2}=\frac{-4-4\sqrt{2}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{2}}{2*-2}=\frac{-4+4\sqrt{2}}{-4}
$