-3x^2+84x-124=0

Solution for -3x^2+84x-124=0 equation:

-3x^2+84x-124=0

a = -3; b = 84; c = -124;
Δ = b2-4ac
Δ = 842-4·(-3)·(-124)
Δ = 5568
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:

$\sqrt{\Delta}=\sqrt{5568}=\sqrt{64*87}=\sqrt{64}*\sqrt{87}=8\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-8\sqrt{87}}{2*-3}=\frac{-84-8\sqrt{87}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+8\sqrt{87}}{2*-3}=\frac{-84+8\sqrt{87}}{-6}
$