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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

24x^2-78x-21=0

a = 24; b = -78; c = -21;
Δ = b2-4ac
Δ = -782-4·24·(-21)
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-90}{2*24}=\frac{-12}{48}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+90}{2*24}=\frac{168}{48}
=3+1/2
$