1/3x+5=3/4x

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



1/3x+5=3/4x
We move all terms to the left:
1/3x+5-(3/4x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 4x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
1/3x-(+3/4x)+5=0
We get rid of parentheses
1/3x-3/4x+5=0
We calculate fractions
4x/12x^2+(-9x)/12x^2+5=0
We multiply all the terms by the denominator
4x+(-9x)+5*12x^2=0
Wy multiply elements
60x^2+4x+(-9x)=0
We get rid of parentheses
60x^2+4x-9x=0
We add all the numbers together, and all the variables
60x^2-5x=0
a = 60; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·60·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*60}=\frac{0}{120} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*60}=\frac{10}{120} =1/12 $

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