(3x+12)(7x-4)=0

Solution for (3x+12)(7x-4)=0 equation:

(3x+12)(7x-4)=0

We multiply parentheses ..

(+21x^2-12x+84x-48)=0

We get rid of parentheses

21x^2-12x+84x-48=0

We add all the numbers together, and all the variables

21x^2+72x-48=0

a = 21; b = 72; c = -48;
Δ = b2-4ac
Δ = 722-4·21·(-48)
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-96}{2*21}=\frac{-168}{42}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+96}{2*21}=\frac{24}{42}
=4/7
$