15x+12x(x-10)=141

Solution for 15x+12x(x-10)=141 equation:

15x+12x(x-10)=141

We move all terms to the left:

15x+12x(x-10)-(141)=0

We multiply parentheses

12x^2+15x-120x-141=0

We add all the numbers together, and all the variables

12x^2-105x-141=0

a = 12; b = -105; c = -141;
Δ = b2-4ac
Δ = -1052-4·12·(-141)
Δ = 17793
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:

$\sqrt{\Delta}=\sqrt{17793}=\sqrt{9*1977}=\sqrt{9}*\sqrt{1977}=3\sqrt{1977}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-3\sqrt{1977}}{2*12}=\frac{105-3\sqrt{1977}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+3\sqrt{1977}}{2*12}=\frac{105+3\sqrt{1977}}{24}
$