8x=9x^2-8

Solution for 8x=9x^2-8 equation:

8x=9x^2-8

We move all terms to the left:

8x-(9x^2-8)=0

We get rid of parentheses

-9x^2+8x+8=0

a = -9; b = 8; c = +8;
Δ = b2-4ac
Δ = 82-4·(-9)·8
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{22}}{2*-9}=\frac{-8-4\sqrt{22}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{22}}{2*-9}=\frac{-8+4\sqrt{22}}{-18}
$