9x(2x-6)=34

Solution for 9x(2x-6)=34 equation:

9x(2x-6)=34

We move all terms to the left:

9x(2x-6)-(34)=0

We multiply parentheses

18x^2-54x-34=0

a = 18; b = -54; c = -34;
Δ = b2-4ac
Δ = -542-4·18·(-34)
Δ = 5364
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:

$\sqrt{\Delta}=\sqrt{5364}=\sqrt{36*149}=\sqrt{36}*\sqrt{149}=6\sqrt{149}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{149}}{2*18}=\frac{54-6\sqrt{149}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{149}}{2*18}=\frac{54+6\sqrt{149}}{36}
$