9x(4x+2)=13

Solution for 9x(4x+2)=13 equation:

9x(4x+2)=13

We move all terms to the left:

9x(4x+2)-(13)=0

We multiply parentheses

36x^2+18x-13=0

a = 36; b = 18; c = -13;
Δ = b2-4ac
Δ = 182-4·36·(-13)
Δ = 2196
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:

$\sqrt{\Delta}=\sqrt{2196}=\sqrt{36*61}=\sqrt{36}*\sqrt{61}=6\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{61}}{2*36}=\frac{-18-6\sqrt{61}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{61}}{2*36}=\frac{-18+6\sqrt{61}}{72}
$