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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

5/6x-(3x+1)=0

We get rid of parentheses

5/6x-3x-1=0

We multiply all the terms by the denominator


-3x*6x-1*6x+5=0

Wy multiply elements

-18x^2-6x+5=0

a = -18; b = -6; c = +5;
Δ = b2-4ac
Δ = -62-4·(-18)·5
Δ = 396
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{11}}{2*-18}=\frac{6-6\sqrt{11}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{11}}{2*-18}=\frac{6+6\sqrt{11}}{-36}
$