(2X+15)(6x-45)=180

Solution for (2X+15)(6x-45)=180 equation:

(2X+15)(6X-45)=180

We move all terms to the left:

(2X+15)(6X-45)-(180)=0

We multiply parentheses ..

(+12X^2-90X+90X-675)-180=0

We get rid of parentheses

12X^2-90X+90X-675-180=0

We add all the numbers together, and all the variables

12X^2-855=0

a = 12; b = 0; c = -855;
Δ = b2-4ac
Δ = 02-4·12·(-855)
Δ = 41040
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:

$\sqrt{\Delta}=\sqrt{41040}=\sqrt{144*285}=\sqrt{144}*\sqrt{285}=12\sqrt{285}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{285}}{2*12}=\frac{0-12\sqrt{285}}{24}
=-\frac{12\sqrt{285}}{24}
=-\frac{\sqrt{285}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{285}}{2*12}=\frac{0+12\sqrt{285}}{24}
=\frac{12\sqrt{285}}{24}
=\frac{\sqrt{285}}{2}
$