2/3x-3/5x=3

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Solution for 2/3x-3/5x=3 equation:



2/3x-3/5x=3
We move all terms to the left:
2/3x-3/5x-(3)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
We calculate fractions
10x/15x^2+(-9x)/15x^2-3=0
We multiply all the terms by the denominator
10x+(-9x)-3*15x^2=0
Wy multiply elements
-45x^2+10x+(-9x)=0
We get rid of parentheses
-45x^2+10x-9x=0
We add all the numbers together, and all the variables
-45x^2+x=0
a = -45; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-45)·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*-45}=\frac{-2}{-90} =1/45 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-45}=\frac{0}{-90} =0 $

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