4x+1+3x+2+3x+7=x(2x+2)

Solution for 4x+1+3x+2+3x+7=x(2x+2) equation:

4x+1+3x+2+3x+7=x(2x+2)

We move all terms to the left:

4x+1+3x+2+3x+7-(x(2x+2))=0

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(x(2x+2)), so:

x(2x+2)

We multiply parentheses

2x^2+2x

Back to the equation:

-(2x^2+2x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2+8x+10=0

a = -2; b = 8; c = +10;
Δ = b2-4ac
Δ = 82-4·(-2)·10
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{-(8)-12}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12}{2*-2}=\frac{4}{-4}
=-1
$