16x+x^2=80

Solution for 16x+x^2=80 equation:

16x+x^2=80

We move all terms to the left:

16x+x^2-(80)=0

a = 1; b = 16; c = -80;
Δ = b2-4ac
Δ = 162-4·1·(-80)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-24}{2*1}=\frac{-40}{2}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+24}{2*1}=\frac{8}{2}
=4
$