-2/3x+8000=-6/5x+9000

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Solution for -2/3x+8000=-6/5x+9000 equation:



-2/3x+8000=-6/5x+9000
We move all terms to the left:
-2/3x+8000-(-6/5x+9000)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 5x+9000)!=0
x∈R
We get rid of parentheses
-2/3x+6/5x-9000+8000=0
We calculate fractions
(-10x)/15x^2+18x/15x^2-9000+8000=0
We add all the numbers together, and all the variables
(-10x)/15x^2+18x/15x^2-1000=0
We multiply all the terms by the denominator
(-10x)+18x-1000*15x^2=0
We add all the numbers together, and all the variables
18x+(-10x)-1000*15x^2=0
Wy multiply elements
-15000x^2+18x+(-10x)=0
We get rid of parentheses
-15000x^2+18x-10x=0
We add all the numbers together, and all the variables
-15000x^2+8x=0
a = -15000; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-15000)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-15000}=\frac{-16}{-30000} =1/1875 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-15000}=\frac{0}{-30000} =0 $

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