x(6x+4)=36

Solution for x(6x+4)=36 equation:

x(6x+4)=36

We move all terms to the left:

x(6x+4)-(36)=0

We multiply parentheses

6x^2+4x-36=0

a = 6; b = 4; c = -36;
Δ = b2-4ac
Δ = 42-4·6·(-36)
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{55}}{2*6}=\frac{-4-4\sqrt{55}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{55}}{2*6}=\frac{-4+4\sqrt{55}}{12}
$