(2a-6)(3a+15)=12

Solution for (2a-6)(3a+15)=12 equation:

(2a-6)(3a+15)=12

We move all terms to the left:

(2a-6)(3a+15)-(12)=0

We multiply parentheses ..

(+6a^2+30a-18a-90)-12=0

We get rid of parentheses

6a^2+30a-18a-90-12=0

We add all the numbers together, and all the variables

6a^2+12a-102=0

a = 6; b = 12; c = -102;
Δ = b2-4ac
Δ = 122-4·6·(-102)
Δ = 2592
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:

$\sqrt{\Delta}=\sqrt{2592}=\sqrt{1296*2}=\sqrt{1296}*\sqrt{2}=36\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-36\sqrt{2}}{2*6}=\frac{-12-36\sqrt{2}}{12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+36\sqrt{2}}{2*6}=\frac{-12+36\sqrt{2}}{12}
$