-40x+8x^2=205

Solution for -40x+8x^2=205 equation:

-40x+8x^2=205

We move all terms to the left:

-40x+8x^2-(205)=0

a = 8; b = -40; c = -205;
Δ = b2-4ac
Δ = -402-4·8·(-205)
Δ = 8160
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:

$\sqrt{\Delta}=\sqrt{8160}=\sqrt{16*510}=\sqrt{16}*\sqrt{510}=4\sqrt{510}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{510}}{2*8}=\frac{40-4\sqrt{510}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{510}}{2*8}=\frac{40+4\sqrt{510}}{16}
$