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

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

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

We multiply parentheses ..

(+16x^2-28x+48x-84)=0

We get rid of parentheses

16x^2-28x+48x-84=0

We add all the numbers together, and all the variables

16x^2+20x-84=0

a = 16; b = 20; c = -84;
Δ = b2-4ac
Δ = 202-4·16·(-84)
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-76}{2*16}=\frac{-96}{32}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+76}{2*16}=\frac{56}{32}
=1+3/4
$