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3/5x-3/10x=3/130
We move all terms to the left:
3/5x-3/10x-(3/130)=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-3/10x-(+3/130)=0
We get rid of parentheses
3/5x-3/10x-3/130=0
We calculate fractions
(-150x^2)/6500x^2+3900x/6500x^2+(-1950x)/6500x^2=0
We multiply all the terms by the denominator
(-150x^2)+3900x+(-1950x)=0
We get rid of parentheses
-150x^2+3900x-1950x=0
We add all the numbers together, and all the variables
-150x^2+1950x=0
a = -150; b = 1950; c = 0;
Δ = b2-4ac
Δ = 19502-4·(-150)·0
Δ = 3802500
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{3802500}=1950$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1950)-1950}{2*-150}=\frac{-3900}{-300} =+13 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1950)+1950}{2*-150}=\frac{0}{-300} =0 $
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