(5x+40)(3x-35)=180

Solution for (5x+40)(3x-35)=180 equation:

(5x+40)(3x-35)=180

We move all terms to the left:

(5x+40)(3x-35)-(180)=0

We multiply parentheses ..

(+15x^2-175x+120x-1400)-180=0

We get rid of parentheses

15x^2-175x+120x-1400-180=0

We add all the numbers together, and all the variables

15x^2-55x-1580=0

a = 15; b = -55; c = -1580;
Δ = b2-4ac
Δ = -552-4·15·(-1580)
Δ = 97825
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:

$\sqrt{\Delta}=\sqrt{97825}=\sqrt{25*3913}=\sqrt{25}*\sqrt{3913}=5\sqrt{3913}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-5\sqrt{3913}}{2*15}=\frac{55-5\sqrt{3913}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+5\sqrt{3913}}{2*15}=\frac{55+5\sqrt{3913}}{30}
$