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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

6x^2+25x-189=0

a = 6; b = 25; c = -189;
Δ = b2-4ac
Δ = 252-4·6·(-189)
Δ = 5161
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{-(25)-\sqrt{5161}}{2*6}=\frac{-25-\sqrt{5161}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{5161}}{2*6}=\frac{-25+\sqrt{5161}}{12}
$