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

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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 $

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