9x2-8=-34x

Solution for 9x2-8=-34x equation:

9x^2-8=-34x

We move all terms to the left:

9x^2-8-(-34x)=0

We get rid of parentheses

9x^2+34x-8=0

a = 9; b = 34; c = -8;
Δ = b2-4ac
Δ = 342-4·9·(-8)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-38}{2*9}=\frac{-72}{18}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+38}{2*9}=\frac{4}{18}
=2/9
$