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

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

X(X+1)=2X+3X

We move all terms to the left:

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

We add all the numbers together, and all the variables

X(X+1)-(+5X)=0

We multiply parentheses

X^2+X-(+5X)=0

We get rid of parentheses

X^2+X-5X=0

We add all the numbers together, and all the variables

X^2-4X=0

a = 1; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·1·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*1}=\frac{0}{2}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*1}=\frac{8}{2}
=4
$