(6x+4)(9x+11)=180

Solution for (6x+4)(9x+11)=180 equation:

(6x+4)(9x+11)=180

We move all terms to the left:

(6x+4)(9x+11)-(180)=0

We multiply parentheses ..

(+54x^2+66x+36x+44)-180=0

We get rid of parentheses

54x^2+66x+36x+44-180=0

We add all the numbers together, and all the variables

54x^2+102x-136=0

a = 54; b = 102; c = -136;
Δ = b2-4ac
Δ = 1022-4·54·(-136)
Δ = 39780
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:

$\sqrt{\Delta}=\sqrt{39780}=\sqrt{36*1105}=\sqrt{36}*\sqrt{1105}=6\sqrt{1105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(102)-6\sqrt{1105}}{2*54}=\frac{-102-6\sqrt{1105}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(102)+6\sqrt{1105}}{2*54}=\frac{-102+6\sqrt{1105}}{108}
$