5x=3x(x+6)

Solution for 5x=3x(x+6) equation:

5x=3x(x+6)

We move all terms to the left:

5x-(3x(x+6))=0


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

3x(x+6)

We multiply parentheses

3x^2+18x

Back to the equation:

-(3x^2+18x)


We get rid of parentheses

-3x^2+5x-18x=0

We add all the numbers together, and all the variables

-3x^2-13x=0

a = -3; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·(-3)·0
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{-(-13)-13}{2*-3}=\frac{0}{-6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*-3}=\frac{26}{-6}
=-4+1/3
$