80x-16x^2=40

Solution for 80x-16x^2=40 equation:

80x-16x^2=40

We move all terms to the left:

80x-16x^2-(40)=0

a = -16; b = 80; c = -40;
Δ = b2-4ac
Δ = 802-4·(-16)·(-40)
Δ = 3840
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:

$\sqrt{\Delta}=\sqrt{3840}=\sqrt{256*15}=\sqrt{256}*\sqrt{15}=16\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-16\sqrt{15}}{2*-16}=\frac{-80-16\sqrt{15}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+16\sqrt{15}}{2*-16}=\frac{-80+16\sqrt{15}}{-32}
$