18x-8x^2=8

Solution for 18x-8x^2=8 equation:

18x-8x^2=8

We move all terms to the left:

18x-8x^2-(8)=0

a = -8; b = 18; c = -8;
Δ = b2-4ac
Δ = 182-4·(-8)·(-8)
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{17}}{2*-8}=\frac{-18-2\sqrt{17}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{17}}{2*-8}=\frac{-18+2\sqrt{17}}{-16}
$