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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

-8x^2+28x-6x+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{-56}{-16}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+34}{2*-8}=\frac{12}{-16}
=-3/4
$