(12x+3)(2x-7)-5x(2x-7)=0

Solution for (12x+3)(2x-7)-5x(2x-7)=0 equation:

(12x+3)(2x-7)-5x(2x-7)=0

We multiply parentheses

-10x^2+(12x+3)(2x-7)+35x=0

We multiply parentheses ..

-10x^2+(+24x^2-84x+6x-21)+35x=0

We get rid of parentheses

-10x^2+24x^2-84x+6x+35x-21=0

We add all the numbers together, and all the variables

14x^2-43x-21=0

a = 14; b = -43; c = -21;
Δ = b2-4ac
Δ = -432-4·14·(-21)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-55}{2*14}=\frac{-12}{28}
=-3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+55}{2*14}=\frac{98}{28}
=3+1/2
$