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3/5x+1/10x=36/15
We move all terms to the left:
3/5x+1/10x-(36/15)=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
3/5x+1/10x-(+36/15)=0
We get rid of parentheses
3/5x+1/10x-36/15=0
We calculate fractions
(-1800x^2)/750x^2+450x/750x^2+75x/750x^2=0
We multiply all the terms by the denominator
(-1800x^2)+450x+75x=0
We add all the numbers together, and all the variables
(-1800x^2)+525x=0
We get rid of parentheses
-1800x^2+525x=0
a = -1800; b = 525; c = 0;
Δ = b2-4ac
Δ = 5252-4·(-1800)·0
Δ = 275625
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{275625}=525$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(525)-525}{2*-1800}=\frac{-1050}{-3600} =7/24 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(525)+525}{2*-1800}=\frac{0}{-3600} =0 $
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