(x-3)(12x-25)=180

Solution for (x-3)(12x-25)=180 equation:

(x-3)(12x-25)=180

We move all terms to the left:

(x-3)(12x-25)-(180)=0

We multiply parentheses ..

(+12x^2-25x-36x+75)-180=0

We get rid of parentheses

12x^2-25x-36x+75-180=0

We add all the numbers together, and all the variables

12x^2-61x-105=0

a = 12; b = -61; c = -105;
Δ = b2-4ac
Δ = -612-4·12·(-105)
Δ = 8761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-61)-\sqrt{8761}}{2*12}=\frac{61-\sqrt{8761}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-61)+\sqrt{8761}}{2*12}=\frac{61+\sqrt{8761}}{24}
$