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-2/5x+1/10x+1=3
We move all terms to the left:
-2/5x+1/10x+1-(3)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 10x!=0We add all the numbers together, and all the variables
x!=0/10
x!=0
x∈R
-2/5x+1/10x-2=0
We calculate fractions
(-20x)/50x^2+5x/50x^2-2=0
We multiply all the terms by the denominator
(-20x)+5x-2*50x^2=0
We add all the numbers together, and all the variables
5x+(-20x)-2*50x^2=0
Wy multiply elements
-100x^2+5x+(-20x)=0
We get rid of parentheses
-100x^2+5x-20x=0
We add all the numbers together, and all the variables
-100x^2-15x=0
a = -100; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-100)·0
Δ = 225
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{225}=15$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*-100}=\frac{0}{-200} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-100}=\frac{30}{-200} =-3/20 $
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