9x2+6x=8

Solution for 9x2+6x=8 equation:

9x^2+6x=8

We move all terms to the left:

9x^2+6x-(8)=0

a = 9; b = 6; c = -8;
Δ = b2-4ac
Δ = 62-4·9·(-8)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-18}{2*9}=\frac{-24}{18}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+18}{2*9}=\frac{12}{18}
=2/3
$