(4x-9)(2x+6)=180

Solution for (4x-9)(2x+6)=180 equation:

(4x-9)(2x+6)=180

We move all terms to the left:

(4x-9)(2x+6)-(180)=0

We multiply parentheses ..

(+8x^2+24x-18x-54)-180=0

We get rid of parentheses

8x^2+24x-18x-54-180=0

We add all the numbers together, and all the variables

8x^2+6x-234=0

a = 8; b = 6; c = -234;
Δ = b2-4ac
Δ = 62-4·8·(-234)
Δ = 7524
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:

$\sqrt{\Delta}=\sqrt{7524}=\sqrt{36*209}=\sqrt{36}*\sqrt{209}=6\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{209}}{2*8}=\frac{-6-6\sqrt{209}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{209}}{2*8}=\frac{-6+6\sqrt{209}}{16}
$