10x+x*x=80

Solution for 10x+x*x=80 equation:

10x+x*x=80

We move all terms to the left:

10x+x*x-(80)=0

Wy multiply elements

x^2+10x-80=0

a = 1; b = 10; c = -80;
Δ = b2-4ac
Δ = 102-4·1·(-80)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{105}}{2*1}=\frac{-10-2\sqrt{105}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{105}}{2*1}=\frac{-10+2\sqrt{105}}{2}
$