2x(4+x)+1=x+1

Solution for 2x(4+x)+1=x+1 equation:

2x(4+x)+1=x+1

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

2x^2+8x-(x+1)+1=0

We get rid of parentheses

2x^2+8x-x-1+1=0

We add all the numbers together, and all the variables

2x^2+7x=0

a = 2; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·2·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*2}=\frac{-14}{4}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*2}=\frac{0}{4}
=0
$