5x^2-65x-60=0

Solution for 5x^2-65x-60=0 equation:

5x^2-65x-60=0

a = 5; b = -65; c = -60;
Δ = b2-4ac
Δ = -652-4·5·(-60)
Δ = 5425
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:

$\sqrt{\Delta}=\sqrt{5425}=\sqrt{25*217}=\sqrt{25}*\sqrt{217}=5\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-5\sqrt{217}}{2*5}=\frac{65-5\sqrt{217}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+5\sqrt{217}}{2*5}=\frac{65+5\sqrt{217}}{10}
$