(2x+7)(2x+1)=0

Solution for (2x+7)(2x+1)=0 equation:

(2x+7)(2x+1)=0

We multiply parentheses ..

(+4x^2+2x+14x+7)=0

We get rid of parentheses

4x^2+2x+14x+7=0

We add all the numbers together, and all the variables

4x^2+16x+7=0

a = 4; b = 16; c = +7;
Δ = b2-4ac
Δ = 162-4·4·7
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-12}{2*4}=\frac{-28}{8}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+12}{2*4}=\frac{-4}{8}
=-1/2
$