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

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

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

We multiply parentheses ..

(+4x^2+6x+14x+21)=0

We get rid of parentheses

4x^2+6x+14x+21=0

We add all the numbers together, and all the variables

4x^2+20x+21=0

a = 4; b = 20; c = +21;
Δ = b2-4ac
Δ = 202-4·4·21
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-8}{2*4}=\frac{-28}{8}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+8}{2*4}=\frac{-12}{8}
=-1+1/2
$