15a^2-5a-35=0

Solution for 15a^2-5a-35=0 equation:

15a^2-5a-35=0

a = 15; b = -5; c = -35;
Δ = b2-4ac
Δ = -52-4·15·(-35)
Δ = 2125
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:

$\sqrt{\Delta}=\sqrt{2125}=\sqrt{25*85}=\sqrt{25}*\sqrt{85}=5\sqrt{85}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{85}}{2*15}=\frac{5-5\sqrt{85}}{30}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{85}}{2*15}=\frac{5+5\sqrt{85}}{30}
$