(8x+2)(9x+3)=180

Solution for (8x+2)(9x+3)=180 equation:

(8x+2)(9x+3)=180

We move all terms to the left:

(8x+2)(9x+3)-(180)=0

We multiply parentheses ..

(+72x^2+24x+18x+6)-180=0

We get rid of parentheses

72x^2+24x+18x+6-180=0

We add all the numbers together, and all the variables

72x^2+42x-174=0

a = 72; b = 42; c = -174;
Δ = b2-4ac
Δ = 422-4·72·(-174)
Δ = 51876
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:

$\sqrt{\Delta}=\sqrt{51876}=\sqrt{36*1441}=\sqrt{36}*\sqrt{1441}=6\sqrt{1441}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6\sqrt{1441}}{2*72}=\frac{-42-6\sqrt{1441}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6\sqrt{1441}}{2*72}=\frac{-42+6\sqrt{1441}}{144}
$