(3x-5)(x+1)=180

Solution for (3x-5)(x+1)=180 equation:

(3x-5)(x+1)=180

We move all terms to the left:

(3x-5)(x+1)-(180)=0

We multiply parentheses ..

(+3x^2+3x-5x-5)-180=0

We get rid of parentheses

3x^2+3x-5x-5-180=0

We add all the numbers together, and all the variables

3x^2-2x-185=0

a = 3; b = -2; c = -185;
Δ = b2-4ac
Δ = -22-4·3·(-185)
Δ = 2224
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:

$\sqrt{\Delta}=\sqrt{2224}=\sqrt{16*139}=\sqrt{16}*\sqrt{139}=4\sqrt{139}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{139}}{2*3}=\frac{2-4\sqrt{139}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{139}}{2*3}=\frac{2+4\sqrt{139}}{6}
$