2(2x+1)(x+5)-(x+5)=0

Solution for 2(2x+1)(x+5)-(x+5)=0 equation:

2(2x+1)(x+5)-(x+5)=0

We get rid of parentheses

2(2x+1)(x+5)-x-5=0

We multiply parentheses ..

2(+2x^2+10x+x+5)-x-5=0

We add all the numbers together, and all the variables

2(+2x^2+10x+x+5)-1x-5=0

We multiply parentheses

4x^2+20x+2x-1x+10-5=0

We add all the numbers together, and all the variables

4x^2+21x+5=0

a = 4; b = 21; c = +5;
Δ = b2-4ac
Δ = 212-4·4·5
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-19}{2*4}=\frac{-40}{8}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+19}{2*4}=\frac{-2}{8}
=-1/4
$