3x/12=5x/x+12

Solution for 3x/12=5x/x+12 equation:

3x/12=5x/x+12

We move all terms to the left:

3x/12-(5x/x+12)=0


Domain of the equation: x+12)!=0

x∈R


We get rid of parentheses

3x/12-5x/x-12=0

We calculate fractions


3x^2/12x+(-60x)/12x-12=0

We multiply all the terms by the denominator


3x^2+(-60x)-12*12x=0

Wy multiply elements

3x^2+(-60x)-144x=0

We get rid of parentheses

3x^2-60x-144x=0

We add all the numbers together, and all the variables

3x^2-204x=0

a = 3; b = -204; c = 0;
Δ = b2-4ac
Δ = -2042-4·3·0
Δ = 41616
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{41616}=204$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-204)-204}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-204)+204}{2*3}=\frac{408}{6}
=68
$