(3x-7)(4x+6)=0

Solution for (3x-7)(4x+6)=0 equation:

(3x-7)(4x+6)=0

We multiply parentheses ..

(+12x^2+18x-28x-42)=0

We get rid of parentheses

12x^2+18x-28x-42=0

We add all the numbers together, and all the variables

12x^2-10x-42=0

a = 12; b = -10; c = -42;
Δ = b2-4ac
Δ = -102-4·12·(-42)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-46}{2*12}=\frac{-36}{24}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+46}{2*12}=\frac{56}{24}
=2+1/3
$