5X/x+12=3x/12

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

5X/X+12=3X/12

We move all terms to the left:

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


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

5X/X-3X/12+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{-408}{-6}
=+68
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(204)+204}{2*-3}=\frac{0}{-6}
=0
$