0=(2x^2)-5x-512

Solution for 0=(2x^2)-5x-512 equation:

0=(2x^2)-5x-512

We move all terms to the left:

0-((2x^2)-5x-512)=0

We add all the numbers together, and all the variables

-(2x^2-5x-512)=0

We get rid of parentheses

-2x^2+5x+512=0

a = -2; b = 5; c = +512;
Δ = b2-4ac
Δ = 52-4·(-2)·512
Δ = 4121
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{-(5)-\sqrt{4121}}{2*-2}=\frac{-5-\sqrt{4121}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{4121}}{2*-2}=\frac{-5+\sqrt{4121}}{-4}
$