(2x+38)(3x-9)=180

Solution for (2x+38)(3x-9)=180 equation:

(2x+38)(3x-9)=180

We move all terms to the left:

(2x+38)(3x-9)-(180)=0

We multiply parentheses ..

(+6x^2-18x+114x-342)-180=0

We get rid of parentheses

6x^2-18x+114x-342-180=0

We add all the numbers together, and all the variables

6x^2+96x-522=0

a = 6; b = 96; c = -522;
Δ = b2-4ac
Δ = 962-4·6·(-522)
Δ = 21744
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:

$\sqrt{\Delta}=\sqrt{21744}=\sqrt{144*151}=\sqrt{144}*\sqrt{151}=12\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-12\sqrt{151}}{2*6}=\frac{-96-12\sqrt{151}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+12\sqrt{151}}{2*6}=\frac{-96+12\sqrt{151}}{12}
$