-14x^2+84x=12

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

-14x^2+84x=12

We move all terms to the left:

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

a = -14; b = 84; c = -12;
Δ = b2-4ac
Δ = 842-4·(-14)·(-12)
Δ = 6384
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:

$\sqrt{\Delta}=\sqrt{6384}=\sqrt{16*399}=\sqrt{16}*\sqrt{399}=4\sqrt{399}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{399}}{2*-14}=\frac{-84-4\sqrt{399}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{399}}{2*-14}=\frac{-84+4\sqrt{399}}{-28}
$