X/3=4x/x+3

Solution for X/3=4x/x+3 equation:

X/3=4X/X+3

We move all terms to the left:

X/3-(4X/X+3)=0


Domain of the equation: X+3)!=0

X∈R


We get rid of parentheses

X/3-4X/X-3=0

We calculate fractions


X^2/3X+(-12X)/3X-3=0

We multiply all the terms by the denominator


X^2+(-12X)-3*3X=0

Wy multiply elements

X^2+(-12X)-9X=0

We get rid of parentheses

X^2-12X-9X=0

We add all the numbers together, and all the variables

X^2-21X=0

a = 1; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·1·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*1}=\frac{0}{2}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*1}=\frac{42}{2}
=21
$