290-2x^2-8x=0

Solution for 290-2x^2-8x=0 equation:

290-2x^2-8x=0

a = -2; b = -8; c = +290;
Δ = b2-4ac
Δ = -82-4·(-2)·290
Δ = 2384
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:

$\sqrt{\Delta}=\sqrt{2384}=\sqrt{16*149}=\sqrt{16}*\sqrt{149}=4\sqrt{149}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{149}}{2*-2}=\frac{8-4\sqrt{149}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{149}}{2*-2}=\frac{8+4\sqrt{149}}{-4}
$