(4x-30)(3x-5)=180

Solution for (4x-30)(3x-5)=180 equation:

(4x-30)(3x-5)=180

We move all terms to the left:

(4x-30)(3x-5)-(180)=0

We multiply parentheses ..

(+12x^2-20x-90x+150)-180=0

We get rid of parentheses

12x^2-20x-90x+150-180=0

We add all the numbers together, and all the variables

12x^2-110x-30=0

a = 12; b = -110; c = -30;
Δ = b2-4ac
Δ = -1102-4·12·(-30)
Δ = 13540
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:

$\sqrt{\Delta}=\sqrt{13540}=\sqrt{4*3385}=\sqrt{4}*\sqrt{3385}=2\sqrt{3385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-2\sqrt{3385}}{2*12}=\frac{110-2\sqrt{3385}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+2\sqrt{3385}}{2*12}=\frac{110+2\sqrt{3385}}{24}
$