4x(x+1)+1+(-x)=10+x

Solution for 4x(x+1)+1+(-x)=10+x equation:

4x(x+1)+1+(-x)=10+x

We move all terms to the left:

4x(x+1)+1+(-x)-(10+x)=0

We add all the numbers together, and all the variables

4x(x+1)+(-1x)-(x+10)+1=0

We multiply parentheses

4x^2+4x+(-1x)-(x+10)+1=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2+2x-9=0

a = 4; b = 2; c = -9;
Δ = b2-4ac
Δ = 22-4·4·(-9)
Δ = 148
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{37}}{2*4}=\frac{-2-2\sqrt{37}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{37}}{2*4}=\frac{-2+2\sqrt{37}}{8}
$