15a^2-75a-5=0

Solution for 15a^2-75a-5=0 equation:

15a^2-75a-5=0

a = 15; b = -75; c = -5;
Δ = b2-4ac
Δ = -752-4·15·(-5)
Δ = 5925
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:

$\sqrt{\Delta}=\sqrt{5925}=\sqrt{25*237}=\sqrt{25}*\sqrt{237}=5\sqrt{237}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-5\sqrt{237}}{2*15}=\frac{75-5\sqrt{237}}{30}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+5\sqrt{237}}{2*15}=\frac{75+5\sqrt{237}}{30}
$