5x^2-50x-20=0

Solution for 5x^2-50x-20=0 equation:

5x^2-50x-20=0

a = 5; b = -50; c = -20;
Δ = b2-4ac
Δ = -502-4·5·(-20)
Δ = 2900
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:

$\sqrt{\Delta}=\sqrt{2900}=\sqrt{100*29}=\sqrt{100}*\sqrt{29}=10\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{29}}{2*5}=\frac{50-10\sqrt{29}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{29}}{2*5}=\frac{50+10\sqrt{29}}{10}
$