10x+x^2=82

Solution for 10x+x^2=82 equation:

10x+x^2=82

We move all terms to the left:

10x+x^2-(82)=0

a = 1; b = 10; c = -82;
Δ = b2-4ac
Δ = 102-4·1·(-82)
Δ = 428
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:

$\sqrt{\Delta}=\sqrt{428}=\sqrt{4*107}=\sqrt{4}*\sqrt{107}=2\sqrt{107}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{107}}{2*1}=\frac{-10-2\sqrt{107}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{107}}{2*1}=\frac{-10+2\sqrt{107}}{2}
$