3/4x+2/3x=1/3x+5

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Solution for 3/4x+2/3x=1/3x+5 equation: 



3/4x+2/3x=1/3x+5

We move all terms to the left:

3/4x+2/3x-(1/3x+5)=0



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R





Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R





Domain of the equation: 3x+5)!=0

x∈R



We get rid of parentheses

3/4x+2/3x-1/3x-5=0

We calculate fractions


9x/12x^2+(-4x+2)/12x^2-5=0

We multiply all the terms by the denominator


9x+(-4x+2)-5*12x^2=0

Wy multiply elements

-60x^2+9x+(-4x+2)=0

We get rid of parentheses

-60x^2+9x-4x+2=0

We add all the numbers together, and all the variables

-60x^2+5x+2=0

a = -60; b = 5; c = +2;
Δ = b2-4ac
Δ = 52-4·(-60)·2
Δ = 505
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{505}}{2*-60}=\frac{-5-\sqrt{505}}{-120}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{505}}{2*-60}=\frac{-5+\sqrt{505}}{-120}
$

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