64x-2x^2=136

Solution for 64x-2x^2=136 equation:

64x-2x^2=136

We move all terms to the left:

64x-2x^2-(136)=0

a = -2; b = 64; c = -136;
Δ = b2-4ac
Δ = 642-4·(-2)·(-136)
Δ = 3008
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:

$\sqrt{\Delta}=\sqrt{3008}=\sqrt{64*47}=\sqrt{64}*\sqrt{47}=8\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-8\sqrt{47}}{2*-2}=\frac{-64-8\sqrt{47}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+8\sqrt{47}}{2*-2}=\frac{-64+8\sqrt{47}}{-4}
$