x=2x^2-24x-64

Solution for x=2x^2-24x-64 equation:

x=2x^2-24x-64

We move all terms to the left:

x-(2x^2-24x-64)=0

We get rid of parentheses

-2x^2+x+24x+64=0

We add all the numbers together, and all the variables

-2x^2+25x+64=0

a = -2; b = 25; c = +64;
Δ = b2-4ac
Δ = 252-4·(-2)·64
Δ = 1137
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{-(25)-\sqrt{1137}}{2*-2}=\frac{-25-\sqrt{1137}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{1137}}{2*-2}=\frac{-25+\sqrt{1137}}{-4}
$