8/3x+35=5/6x+46

Solution for 8/3x+35=5/6x+46 equation:

8/3x+35=5/6x+46

We move all terms to the left:

8/3x+35-(5/6x+46)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x+46)!=0

x∈R


We get rid of parentheses

8/3x-5/6x-46+35=0

We calculate fractions


48x/18x^2+(-15x)/18x^2-46+35=0

We add all the numbers together, and all the variables

48x/18x^2+(-15x)/18x^2-11=0

We multiply all the terms by the denominator


48x+(-15x)-11*18x^2=0

Wy multiply elements

-198x^2+48x+(-15x)=0

We get rid of parentheses

-198x^2+48x-15x=0

We add all the numbers together, and all the variables

-198x^2+33x=0

a = -198; b = 33; c = 0;
Δ = b2-4ac
Δ = 332-4·(-198)·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-33}{2*-198}=\frac{-66}{-396}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+33}{2*-198}=\frac{0}{-396}
=0
$