(4x+1)(x+1)=1

Solution for (4x+1)(x+1)=1 equation:

(4x+1)(x+1)=1

We move all terms to the left:

(4x+1)(x+1)-(1)=0

We multiply parentheses ..

(+4x^2+4x+x+1)-1=0

We get rid of parentheses

4x^2+4x+x+1-1=0

We add all the numbers together, and all the variables

4x^2+5x=0

a = 4; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·4·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*4}=\frac{-10}{8}
=-1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*4}=\frac{0}{8}
=0
$