40x-16x^2=8

Solution for 40x-16x^2=8 equation:

40x-16x^2=8

We move all terms to the left:

40x-16x^2-(8)=0

a = -16; b = 40; c = -8;
Δ = b2-4ac
Δ = 402-4·(-16)·(-8)
Δ = 1088
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:

$\sqrt{\Delta}=\sqrt{1088}=\sqrt{64*17}=\sqrt{64}*\sqrt{17}=8\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-8\sqrt{17}}{2*-16}=\frac{-40-8\sqrt{17}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+8\sqrt{17}}{2*-16}=\frac{-40+8\sqrt{17}}{-32}
$