(7+2x)(3-4x)=0

Solution for (7+2x)(3-4x)=0 equation:

(7+2x)(3-4x)=0

We add all the numbers together, and all the variables

(2x+7)(-4x+3)=0

We multiply parentheses ..

(-8x^2+6x-28x+21)=0

We get rid of parentheses

-8x^2+6x-28x+21=0

We add all the numbers together, and all the variables

-8x^2-22x+21=0

a = -8; b = -22; c = +21;
Δ = b2-4ac
Δ = -222-4·(-8)·21
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-34}{2*-8}=\frac{-12}{-16}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+34}{2*-8}=\frac{56}{-16}
=-3+1/2
$