5x^2-50x+108=0

Solution for 5x^2-50x+108=0 equation:

5x^2-50x+108=0

a = 5; b = -50; c = +108;
Δ = b2-4ac
Δ = -502-4·5·108
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{85}}{2*5}=\frac{50-2\sqrt{85}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{85}}{2*5}=\frac{50+2\sqrt{85}}{10}
$