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

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

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

We multiply parentheses ..

(+36x^2-84x+9x-21)=0

We get rid of parentheses

36x^2-84x+9x-21=0

We add all the numbers together, and all the variables

36x^2-75x-21=0

a = 36; b = -75; c = -21;
Δ = b2-4ac
Δ = -752-4·36·(-21)
Δ = 8649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8649}=93$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-93}{2*36}=\frac{-18}{72}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+93}{2*36}=\frac{168}{72}
=2+1/3
$