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

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



1/3x-2=1/4x+5
We move all terms to the left:
1/3x-2-(1/4x+5)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 4x+5)!=0
x∈R
We get rid of parentheses
1/3x-1/4x-5-2=0
We calculate fractions
4x/12x^2+(-3x)/12x^2-5-2=0
We add all the numbers together, and all the variables
4x/12x^2+(-3x)/12x^2-7=0
We multiply all the terms by the denominator
4x+(-3x)-7*12x^2=0
Wy multiply elements
-84x^2+4x+(-3x)=0
We get rid of parentheses
-84x^2+4x-3x=0
We add all the numbers together, and all the variables
-84x^2+x=0
a = -84; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-84)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-84}=\frac{-2}{-168} =1/84 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-84}=\frac{0}{-168} =0 $

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