(5x-35)(3x+2)=180

Solution for (5x-35)(3x+2)=180 equation:

(5x-35)(3x+2)=180

We move all terms to the left:

(5x-35)(3x+2)-(180)=0

We multiply parentheses ..

(+15x^2+10x-105x-70)-180=0

We get rid of parentheses

15x^2+10x-105x-70-180=0

We add all the numbers together, and all the variables

15x^2-95x-250=0

a = 15; b = -95; c = -250;
Δ = b2-4ac
Δ = -952-4·15·(-250)
Δ = 24025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24025}=155$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-95)-155}{2*15}=\frac{-60}{30}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-95)+155}{2*15}=\frac{250}{30}
=8+1/3
$