x^2-24x=80=0

Solution for x^2-24x=80=0 equation:

x^2-24x=80=0

We move all terms to the left:

x^2-24x-(80)=0

a = 1; b = -24; c = -80;
Δ = b2-4ac
Δ = -242-4·1·(-80)
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{14}}{2*1}=\frac{24-8\sqrt{14}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{14}}{2*1}=\frac{24+8\sqrt{14}}{2}
$