(6x+8)(9x+7)=180

Solution for (6x+8)(9x+7)=180 equation:

(6x+8)(9x+7)=180

We move all terms to the left:

(6x+8)(9x+7)-(180)=0

We multiply parentheses ..

(+54x^2+42x+72x+56)-180=0

We get rid of parentheses

54x^2+42x+72x+56-180=0

We add all the numbers together, and all the variables

54x^2+114x-124=0

a = 54; b = 114; c = -124;
Δ = b2-4ac
Δ = 1142-4·54·(-124)
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{-(114)-6\sqrt{1105}}{2*54}=\frac{-114-6\sqrt{1105}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(114)+6\sqrt{1105}}{2*54}=\frac{-114+6\sqrt{1105}}{108}
$