84x-4x^2=264

Solution for 84x-4x^2=264 equation:

84x-4x^2=264

We move all terms to the left:

84x-4x^2-(264)=0

a = -4; b = 84; c = -264;
Δ = b2-4ac
Δ = 842-4·(-4)·(-264)
Δ = 2832
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:

$\sqrt{\Delta}=\sqrt{2832}=\sqrt{16*177}=\sqrt{16}*\sqrt{177}=4\sqrt{177}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{177}}{2*-4}=\frac{-84-4\sqrt{177}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{177}}{2*-4}=\frac{-84+4\sqrt{177}}{-8}
$