12x^2+84x-15=0

Solution for 12x^2+84x-15=0 equation:

12x^2+84x-15=0

a = 12; b = 84; c = -15;
Δ = b2-4ac
Δ = 842-4·12·(-15)
Δ = 7776
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:

$\sqrt{\Delta}=\sqrt{7776}=\sqrt{1296*6}=\sqrt{1296}*\sqrt{6}=36\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-36\sqrt{6}}{2*12}=\frac{-84-36\sqrt{6}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+36\sqrt{6}}{2*12}=\frac{-84+36\sqrt{6}}{24}
$