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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


We calculate terms in parentheses: -(4(x+2)), so:

4(x+2)

We multiply parentheses

4x+8

Back to the equation:

-(4x+8)


We add all the numbers together, and all the variables

2x^2+5x-(4x+8)+1=0

We get rid of parentheses

2x^2+5x-4x-8+1=0

We add all the numbers together, and all the variables

2x^2+x-7=0

a = 2; b = 1; c = -7;
Δ = b2-4ac
Δ = 12-4·2·(-7)
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{57}}{2*2}=\frac{-1-\sqrt{57}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{57}}{2*2}=\frac{-1+\sqrt{57}}{4}
$