5a^2+8a-60=0

Solution for 5a^2+8a-60=0 equation:

5a^2+8a-60=0

a = 5; b = 8; c = -60;
Δ = b2-4ac
Δ = 82-4·5·(-60)
Δ = 1264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1264}=\sqrt{16*79}=\sqrt{16}*\sqrt{79}=4\sqrt{79}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{79}}{2*5}=\frac{-8-4\sqrt{79}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{79}}{2*5}=\frac{-8+4\sqrt{79}}{10}
$