x/3=7x/12x-5

Solution for x/3=7x/12x-5 equation:

x/3=7x/12x-5

We move all terms to the left:

x/3-(7x/12x-5)=0


Domain of the equation: 12x-5)!=0

x∈R


We get rid of parentheses

x/3-7x/12x+5=0

We calculate fractions


12x^2/36x+(-21x)/36x+5=0

We multiply all the terms by the denominator


12x^2+(-21x)+5*36x=0

Wy multiply elements

12x^2+(-21x)+180x=0

We get rid of parentheses

12x^2-21x+180x=0

We add all the numbers together, and all the variables

12x^2+159x=0

a = 12; b = 159; c = 0;
Δ = b2-4ac
Δ = 1592-4·12·0
Δ = 25281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25281}=159$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(159)-159}{2*12}=\frac{-318}{24}
=-13+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(159)+159}{2*12}=\frac{0}{24}
=0
$