X^2-40x+136=0

Solution for X^2-40x+136=0 equation:

X^2-40X+136=0

a = 1; b = -40; c = +136;
Δ = b2-4ac
Δ = -402-4·1·136
Δ = 1056
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:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{66}}{2*1}=\frac{40-4\sqrt{66}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{66}}{2*1}=\frac{40+4\sqrt{66}}{2}
$