(5x-1)(x+3)=x(x+3)

Solution for (5x-1)(x+3)=x(x+3) equation:

(5x-1)(x+3)=x(x+3)

We move all terms to the left:

(5x-1)(x+3)-(x(x+3))=0

We multiply parentheses ..

(+5x^2+15x-1x-3)-(x(x+3))=0


We calculate terms in parentheses: -(x(x+3)), so:

x(x+3)

We multiply parentheses

x^2+3x

Back to the equation:

-(x^2+3x)


We get rid of parentheses

5x^2-x^2+15x-1x-3x-3=0

We add all the numbers together, and all the variables

4x^2+11x-3=0

a = 4; b = 11; c = -3;
Δ = b2-4ac
Δ = 112-4·4·(-3)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-13}{2*4}=\frac{-24}{8}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+13}{2*4}=\frac{2}{8}
=1/4
$