5-11x^2=8x

Solution for 5-11x^2=8x equation:

5-11x^2=8x

We move all terms to the left:

5-11x^2-(8x)=0

a = -11; b = -8; c = +5;
Δ = b2-4ac
Δ = -82-4·(-11)·5
Δ = 284
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:

$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{71}}{2*-11}=\frac{8-2\sqrt{71}}{-22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{71}}{2*-11}=\frac{8+2\sqrt{71}}{-22}
$