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5/r+2/7r=1
We move all terms to the left:
5/r+2/7r-(1)=0
Domain of the equation: r!=0
r∈R
Domain of the equation: 7r!=0We calculate fractions
r!=0/7
r!=0
r∈R
35r/7r^2+2r/7r^2-1=0
We multiply all the terms by the denominator
35r+2r-1*7r^2=0
We add all the numbers together, and all the variables
37r-1*7r^2=0
Wy multiply elements
-7r^2+37r=0
a = -7; b = 37; c = 0;
Δ = b2-4ac
Δ = 372-4·(-7)·0
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{1369}=37$$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-37}{2*-7}=\frac{-74}{-14} =5+2/7 $$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+37}{2*-7}=\frac{0}{-14} =0 $
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