0.5x^2-36x=522

Solution for 0.5x^2-36x=522 equation:

0.5x^2-36x=522

We move all terms to the left:

0.5x^2-36x-(522)=0

a = 0.5; b = -36; c = -522;
Δ = b2-4ac
Δ = -362-4·0.5·(-522)
Δ = 2340
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:

$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{65}}{2*0.5}=\frac{36-6\sqrt{65}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{65}}{2*0.5}=\frac{36+6\sqrt{65}}{1}
$