15x^2-75x-315=0

Solution for 15x^2-75x-315=0 equation:

15x^2-75x-315=0

a = 15; b = -75; c = -315;
Δ = b2-4ac
Δ = -752-4·15·(-315)
Δ = 24525
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:

$\sqrt{\Delta}=\sqrt{24525}=\sqrt{225*109}=\sqrt{225}*\sqrt{109}=15\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-15\sqrt{109}}{2*15}=\frac{75-15\sqrt{109}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+15\sqrt{109}}{2*15}=\frac{75+15\sqrt{109}}{30}
$