5x^2-50x-62.5=0

Solution for 5x^2-50x-62.5=0 equation:

5x^2-50x-62.5=0

a = 5; b = -50; c = -62.5;
Δ = b2-4ac
Δ = -502-4·5·(-62.5)
Δ = 3750
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:

$\sqrt{\Delta}=\sqrt{3750}=\sqrt{625*6}=\sqrt{625}*\sqrt{6}=25\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-25\sqrt{6}}{2*5}=\frac{50-25\sqrt{6}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+25\sqrt{6}}{2*5}=\frac{50+25\sqrt{6}}{10}
$