X/3=12x/5x-1

Solution for X/3=12x/5x-1 equation:

X/3=12X/5X-1

We move all terms to the left:

X/3-(12X/5X-1)=0


Domain of the equation: 5X-1)!=0

X∈R


We get rid of parentheses

X/3-12X/5X+1=0

We calculate fractions


5X^2/15X+(-36X)/15X+1=0

We multiply all the terms by the denominator


5X^2+(-36X)+1*15X=0

Wy multiply elements

5X^2+(-36X)+15X=0

We get rid of parentheses

5X^2-36X+15X=0

We add all the numbers together, and all the variables

5X^2-21X=0

a = 5; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·5·0
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*5}=\frac{0}{10}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*5}=\frac{42}{10}
=4+1/5
$