X^2-32x+80=0

Solution for X^2-32x+80=0 equation:

X^2-32X+80=0

a = 1; b = -32; c = +80;
Δ = b2-4ac
Δ = -322-4·1·80
Δ = 704
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:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{11}}{2*1}=\frac{32-8\sqrt{11}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{11}}{2*1}=\frac{32+8\sqrt{11}}{2}
$