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

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

(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
$