(4a-33)(2a+15)=180

Solution for (4a-33)(2a+15)=180 equation:

(4a-33)(2a+15)=180

We move all terms to the left:

(4a-33)(2a+15)-(180)=0

We multiply parentheses ..

(+8a^2+60a-66a-495)-180=0

We get rid of parentheses

8a^2+60a-66a-495-180=0

We add all the numbers together, and all the variables

8a^2-6a-675=0

a = 8; b = -6; c = -675;
Δ = b2-4ac
Δ = -62-4·8·(-675)
Δ = 21636
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{21636}=\sqrt{36*601}=\sqrt{36}*\sqrt{601}=6\sqrt{601}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{601}}{2*8}=\frac{6-6\sqrt{601}}{16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{601}}{2*8}=\frac{6+6\sqrt{601}}{16}
$