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3/5x-2/3x=1/10
We move all terms to the left:
3/5x-2/3x-(1/10)=0
Domain of the equation: 5x!=0
x!=0/5
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
3/5x-2/3x-(+1/10)=0
We get rid of parentheses
3/5x-2/3x-1/10=0
We calculate fractions
(-45x^2)/150x^2+90x/150x^2+(-100x)/150x^2=0
We multiply all the terms by the denominator
(-45x^2)+90x+(-100x)=0
We get rid of parentheses
-45x^2+90x-100x=0
We add all the numbers together, and all the variables
-45x^2-10x=0
a = -45; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-45)·0
Δ = 100
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{100}=10$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-45}=\frac{0}{-90} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-45}=\frac{20}{-90} =-2/9 $
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