3/5x+5/6=7/12x+4

Solution for 3/5x+5/6=7/12x+4 equation:

3/5x+5/6=7/12x+4

We move all terms to the left:

3/5x+5/6-(7/12x+4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 12x+4)!=0

x∈R


We get rid of parentheses

3/5x-7/12x-4+5/6=0

We calculate fractions


300x^2/2160x^2+1296x/2160x^2+(-1260x)/2160x^2-4=0

We multiply all the terms by the denominator


300x^2+1296x+(-1260x)-4*2160x^2=0

Wy multiply elements

300x^2-8640x^2+1296x+(-1260x)=0

We get rid of parentheses

300x^2-8640x^2+1296x-1260x=0

We add all the numbers together, and all the variables

-8340x^2+36x=0

a = -8340; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-8340)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-8340}=\frac{-72}{-16680}
=3/695
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-8340}=\frac{0}{-16680}
=0
$