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10/x=5/2x+60
We move all terms to the left:
10/x-(5/2x+60)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 2x+60)!=0We get rid of parentheses
x∈R
10/x-5/2x-60=0
We calculate fractions
20x/2x^2+(-5x)/2x^2-60=0
We multiply all the terms by the denominator
20x+(-5x)-60*2x^2=0
Wy multiply elements
-120x^2+20x+(-5x)=0
We get rid of parentheses
-120x^2+20x-5x=0
We add all the numbers together, and all the variables
-120x^2+15x=0
a = -120; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-120)·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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-120}=\frac{-30}{-240} =1/8 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-120}=\frac{0}{-240} =0 $
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