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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

2x(x+1)-(-1x+5)=0

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2+3x-5=0

a = 2; b = 3; c = -5;
Δ = b2-4ac
Δ = 32-4·2·(-5)
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{-(3)-7}{2*2}=\frac{-10}{4}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+7}{2*2}=\frac{4}{4}
=1
$