15x^2-84x-63=0

Solution for 15x^2-84x-63=0 equation:

15x^2-84x-63=0

a = 15; b = -84; c = -63;
Δ = b2-4ac
Δ = -842-4·15·(-63)
Δ = 10836
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:

$\sqrt{\Delta}=\sqrt{10836}=\sqrt{36*301}=\sqrt{36}*\sqrt{301}=6\sqrt{301}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-6\sqrt{301}}{2*15}=\frac{84-6\sqrt{301}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+6\sqrt{301}}{2*15}=\frac{84+6\sqrt{301}}{30}
$