x^2-82x+432=0

Solution for x^2-82x+432=0 equation:

x^2-82x+432=0

a = 1; b = -82; c = +432;
Δ = b2-4ac
Δ = -822-4·1·432
Δ = 4996
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:

$\sqrt{\Delta}=\sqrt{4996}=\sqrt{4*1249}=\sqrt{4}*\sqrt{1249}=2\sqrt{1249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-2\sqrt{1249}}{2*1}=\frac{82-2\sqrt{1249}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+2\sqrt{1249}}{2*1}=\frac{82+2\sqrt{1249}}{2}
$