4(x+9)x=6

Solution for 4(x+9)x=6 equation:

4(x+9)x=6

We move all terms to the left:

4(x+9)x-(6)=0

We multiply parentheses

4x^2+36x-6=0

a = 4; b = 36; c = -6;
Δ = b2-4ac
Δ = 362-4·4·(-6)
Δ = 1392
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:

$\sqrt{\Delta}=\sqrt{1392}=\sqrt{16*87}=\sqrt{16}*\sqrt{87}=4\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{87}}{2*4}=\frac{-36-4\sqrt{87}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{87}}{2*4}=\frac{-36+4\sqrt{87}}{8}
$