2/3x+8=1/4x-2

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Solution for 2/3x+8=1/4x-2 equation:



2/3x+8=1/4x-2
We move all terms to the left:
2/3x+8-(1/4x-2)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 4x-2)!=0
x∈R
We get rid of parentheses
2/3x-1/4x+2+8=0
We calculate fractions
8x/12x^2+(-3x)/12x^2+2+8=0
We add all the numbers together, and all the variables
8x/12x^2+(-3x)/12x^2+10=0
We multiply all the terms by the denominator
8x+(-3x)+10*12x^2=0
Wy multiply elements
120x^2+8x+(-3x)=0
We get rid of parentheses
120x^2+8x-3x=0
We add all the numbers together, and all the variables
120x^2+5x=0
a = 120; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·120·0
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*120}=\frac{-10}{240} =-1/24 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*120}=\frac{0}{240} =0 $

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