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

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

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

We multiply parentheses ..

(+12x^2+9x-28x-21)=0

We get rid of parentheses

12x^2+9x-28x-21=0

We add all the numbers together, and all the variables

12x^2-19x-21=0

a = 12; b = -19; c = -21;
Δ = b2-4ac
Δ = -192-4·12·(-21)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-37}{2*12}=\frac{-18}{24}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+37}{2*12}=\frac{56}{24}
=2+1/3
$