-14x^2+84x+12=0

Solution for -14x^2+84x+12=0 equation:

-14x^2+84x+12=0

a = -14; b = 84; c = +12;
Δ = b2-4ac
Δ = 842-4·(-14)·12
Δ = 7728
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:

$\sqrt{\Delta}=\sqrt{7728}=\sqrt{16*483}=\sqrt{16}*\sqrt{483}=4\sqrt{483}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{483}}{2*-14}=\frac{-84-4\sqrt{483}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{483}}{2*-14}=\frac{-84+4\sqrt{483}}{-28}
$