(2x+9)(3x+1)=180

Solution for (2x+9)(3x+1)=180 equation:

(2x+9)(3x+1)=180

We move all terms to the left:

(2x+9)(3x+1)-(180)=0

We multiply parentheses ..

(+6x^2+2x+27x+9)-180=0

We get rid of parentheses

6x^2+2x+27x+9-180=0

We add all the numbers together, and all the variables

6x^2+29x-171=0

a = 6; b = 29; c = -171;
Δ = b2-4ac
Δ = 292-4·6·(-171)
Δ = 4945
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-\sqrt{4945}}{2*6}=\frac{-29-\sqrt{4945}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+\sqrt{4945}}{2*6}=\frac{-29+\sqrt{4945}}{12}
$