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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

x^2+2x-x+3x-3-1=0

We add all the numbers together, and all the variables

x^2+4x-4=0

a = 1; b = 4; c = -4;
Δ = b2-4ac
Δ = 42-4·1·(-4)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{2}}{2*1}=\frac{-4-4\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{2}}{2*1}=\frac{-4+4\sqrt{2}}{2}
$