39x=12x(x+4)

Solution for 39x=12x(x+4) equation:

39x=12x(x+4)

We move all terms to the left:

39x-(12x(x+4))=0


We calculate terms in parentheses: -(12x(x+4)), so:

12x(x+4)

We multiply parentheses

12x^2+48x

Back to the equation:

-(12x^2+48x)


We get rid of parentheses

-12x^2+39x-48x=0

We add all the numbers together, and all the variables

-12x^2-9x=0

a = -12; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-12)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-12}=\frac{18}{-24}
=-3/4
$