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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


240x^2/1728x^2+1296x/1728x^2+(-1008x)/1728x^2-4=0

We multiply all the terms by the denominator


240x^2+1296x+(-1008x)-4*1728x^2=0

Wy multiply elements

240x^2-6912x^2+1296x+(-1008x)=0

We get rid of parentheses

240x^2-6912x^2+1296x-1008x=0

We add all the numbers together, and all the variables

-6672x^2+288x=0

a = -6672; b = 288; c = 0;
Δ = b2-4ac
Δ = 2882-4·(-6672)·0
Δ = 82944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{82944}=288$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(288)-288}{2*-6672}=\frac{-576}{-13344}
=6/139
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(288)+288}{2*-6672}=\frac{0}{-13344}
=0
$