(8x+6)(9x-30)=180

Solution for (8x+6)(9x-30)=180 equation:

(8x+6)(9x-30)=180

We move all terms to the left:

(8x+6)(9x-30)-(180)=0

We multiply parentheses ..

(+72x^2-240x+54x-180)-180=0

We get rid of parentheses

72x^2-240x+54x-180-180=0

We add all the numbers together, and all the variables

72x^2-186x-360=0

a = 72; b = -186; c = -360;
Δ = b2-4ac
Δ = -1862-4·72·(-360)
Δ = 138276
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:

$\sqrt{\Delta}=\sqrt{138276}=\sqrt{36*3841}=\sqrt{36}*\sqrt{3841}=6\sqrt{3841}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-186)-6\sqrt{3841}}{2*72}=\frac{186-6\sqrt{3841}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-186)+6\sqrt{3841}}{2*72}=\frac{186+6\sqrt{3841}}{144}
$