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8/9x+1/3x=1/10
We move all terms to the left:
8/9x+1/3x-(1/10)=0
Domain of the equation: 9x!=0
x!=0/9
x!=0
x∈R
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
8/9x+1/3x-(+1/10)=0
We get rid of parentheses
8/9x+1/3x-1/10=0
We calculate fractions
(-81x^2)/270x^2+240x/270x^2+90x/270x^2=0
We multiply all the terms by the denominator
(-81x^2)+240x+90x=0
We add all the numbers together, and all the variables
(-81x^2)+330x=0
We get rid of parentheses
-81x^2+330x=0
a = -81; b = 330; c = 0;
Δ = b2-4ac
Δ = 3302-4·(-81)·0
Δ = 108900
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{108900}=330$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(330)-330}{2*-81}=\frac{-660}{-162} =4+2/27 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(330)+330}{2*-81}=\frac{0}{-162} =0 $
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