13x+x^2=32

Solution for 13x+x^2=32 equation:

13x+x^2=32

We move all terms to the left:

13x+x^2-(32)=0

a = 1; b = 13; c = -32;
Δ = b2-4ac
Δ = 132-4·1·(-32)
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-3\sqrt{33}}{2*1}=\frac{-13-3\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+3\sqrt{33}}{2*1}=\frac{-13+3\sqrt{33}}{2}
$