40x-16x^2=15

Solution for 40x-16x^2=15 equation:

40x-16x^2=15

We move all terms to the left:

40x-16x^2-(15)=0

a = -16; b = 40; c = -15;
Δ = b2-4ac
Δ = 402-4·(-16)·(-15)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-8\sqrt{10}}{2*-16}=\frac{-40-8\sqrt{10}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+8\sqrt{10}}{2*-16}=\frac{-40+8\sqrt{10}}{-32}
$