(6x+7)(3x-35)=180

Solution for (6x+7)(3x-35)=180 equation:

(6x+7)(3x-35)=180

We move all terms to the left:

(6x+7)(3x-35)-(180)=0

We multiply parentheses ..

(+18x^2-210x+21x-245)-180=0

We get rid of parentheses

18x^2-210x+21x-245-180=0

We add all the numbers together, and all the variables

18x^2-189x-425=0

a = 18; b = -189; c = -425;
Δ = b2-4ac
Δ = -1892-4·18·(-425)
Δ = 66321
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:

$\sqrt{\Delta}=\sqrt{66321}=\sqrt{9*7369}=\sqrt{9}*\sqrt{7369}=3\sqrt{7369}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-189)-3\sqrt{7369}}{2*18}=\frac{189-3\sqrt{7369}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-189)+3\sqrt{7369}}{2*18}=\frac{189+3\sqrt{7369}}{36}
$