14x+x^2=529

Solution for 14x+x^2=529 equation:

14x+x^2=529

We move all terms to the left:

14x+x^2-(529)=0

a = 1; b = 14; c = -529;
Δ = b2-4ac
Δ = 142-4·1·(-529)
Δ = 2312
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:

$\sqrt{\Delta}=\sqrt{2312}=\sqrt{1156*2}=\sqrt{1156}*\sqrt{2}=34\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-34\sqrt{2}}{2*1}=\frac{-14-34\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+34\sqrt{2}}{2*1}=\frac{-14+34\sqrt{2}}{2}
$