8/5x-2/3x=3/15

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Solution for 8/5x-2/3x=3/15 equation:



8/5x-2/3x=3/15
We move all terms to the left:
8/5x-2/3x-(3/15)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We add all the numbers together, and all the variables
8/5x-2/3x-(+3/15)=0
We get rid of parentheses
8/5x-2/3x-3/15=0
We calculate fractions
(-135x^2)/225x^2+360x/225x^2+(-150x)/225x^2=0
We multiply all the terms by the denominator
(-135x^2)+360x+(-150x)=0
We get rid of parentheses
-135x^2+360x-150x=0
We add all the numbers together, and all the variables
-135x^2+210x=0
a = -135; b = 210; c = 0;
Δ = b2-4ac
Δ = 2102-4·(-135)·0
Δ = 44100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{44100}=210$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(210)-210}{2*-135}=\frac{-420}{-270} =1+5/9 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(210)+210}{2*-135}=\frac{0}{-270} =0 $

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