11x=8x^2-3

Solution for 11x=8x^2-3 equation:

11x=8x^2-3

We move all terms to the left:

11x-(8x^2-3)=0

We get rid of parentheses

-8x^2+11x+3=0

a = -8; b = 11; c = +3;
Δ = b2-4ac
Δ = 112-4·(-8)·3
Δ = 217
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{217}}{2*-8}=\frac{-11-\sqrt{217}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{217}}{2*-8}=\frac{-11+\sqrt{217}}{-16}
$