527=2x^2-3x

Solution for 527=2x^2-3x equation:

527=2x^2-3x

We move all terms to the left:

527-(2x^2-3x)=0

We get rid of parentheses

-2x^2+3x+527=0

a = -2; b = 3; c = +527;
Δ = b2-4ac
Δ = 32-4·(-2)·527
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-65}{2*-2}=\frac{-68}{-4}
=+17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+65}{2*-2}=\frac{62}{-4}
=-15+1/2
$