60^2+x^2=80^2

Solution for 60^2+x^2=80^2 equation:

60^2+x^2=80^2

We move all terms to the left:

60^2+x^2-(80^2)=0

We add all the numbers together, and all the variables

x^2-2800=0

a = 1; b = 0; c = -2800;
Δ = b2-4ac
Δ = 02-4·1·(-2800)
Δ = 11200
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:

$\sqrt{\Delta}=\sqrt{11200}=\sqrt{1600*7}=\sqrt{1600}*\sqrt{7}=40\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{7}}{2*1}=\frac{0-40\sqrt{7}}{2}
=-\frac{40\sqrt{7}}{2}
=-20\sqrt{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{7}}{2*1}=\frac{0+40\sqrt{7}}{2}
=\frac{40\sqrt{7}}{2}
=20\sqrt{7}
$