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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We multiply parentheses ..

x^2-((+2x^2+6x-1x-3))+3x=0


We calculate terms in parentheses: -((+2x^2+6x-1x-3)), so:

(+2x^2+6x-1x-3)

We get rid of parentheses

2x^2+6x-1x-3

We add all the numbers together, and all the variables

2x^2+5x-3

Back to the equation:

-(2x^2+5x-3)


We add all the numbers together, and all the variables

x^2+3x-(2x^2+5x-3)=0

We get rid of parentheses

x^2-2x^2+3x-5x+3=0

We add all the numbers together, and all the variables

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

a = -1; b = -2; c = +3;
Δ = b2-4ac
Δ = -22-4·(-1)·3
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{-(-2)-4}{2*-1}=\frac{-2}{-2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4}{2*-1}=\frac{6}{-2}
=-3
$