2/3x=4/5x+2

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



2/3x=4/5x+2
We move all terms to the left:
2/3x-(4/5x+2)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 5x+2)!=0
x∈R
We get rid of parentheses
2/3x-4/5x-2=0
We calculate fractions
10x/15x^2+(-12x)/15x^2-2=0
We multiply all the terms by the denominator
10x+(-12x)-2*15x^2=0
Wy multiply elements
-30x^2+10x+(-12x)=0
We get rid of parentheses
-30x^2+10x-12x=0
We add all the numbers together, and all the variables
-30x^2-2x=0
a = -30; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-30)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-30}=\frac{0}{-60} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-30}=\frac{4}{-60} =-1/15 $

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