32x+x^2=504

Solution for 32x+x^2=504 equation:

32x+x^2=504

We move all terms to the left:

32x+x^2-(504)=0

a = 1; b = 32; c = -504;
Δ = b2-4ac
Δ = 322-4·1·(-504)
Δ = 3040
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:

$\sqrt{\Delta}=\sqrt{3040}=\sqrt{16*190}=\sqrt{16}*\sqrt{190}=4\sqrt{190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{190}}{2*1}=\frac{-32-4\sqrt{190}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{190}}{2*1}=\frac{-32+4\sqrt{190}}{2}
$