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

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

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

We multiply parentheses ..

2(+2x^2-3x+14x-21)=0

We multiply parentheses

4x^2-6x+28x-42=0

We add all the numbers together, and all the variables

4x^2+22x-42=0

a = 4; b = 22; c = -42;
Δ = b2-4ac
Δ = 222-4·4·(-42)
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*4}=\frac{-56}{8}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+34}{2*4}=\frac{12}{8}
=1+1/2
$