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5/60.2r+0.75=0.5r
We move all terms to the left:
5/60.2r+0.75-(0.5r)=0
Domain of the equation: 60.2r!=0We add all the numbers together, and all the variables
r!=0/60.2
r!=0
r∈R
5/60.2r-(+0.5r)+0.75=0
We get rid of parentheses
5/60.2r-0.5r+0.75=0
We multiply all the terms by the denominator
-(0.5r)*60.2r+(0.75)*60.2r+5=0
We add all the numbers together, and all the variables
-(+0.5r)*60.2r+(0.75)*60.2r+5=0
We multiply parentheses
-0r^2+45r+5=0
We add all the numbers together, and all the variables
-1r^2+45r+5=0
a = -1; b = 45; c = +5;
Δ = b2-4ac
Δ = 452-4·(-1)·5
Δ = 2045
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}$$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-\sqrt{2045}}{2*-1}=\frac{-45-\sqrt{2045}}{-2} $$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2045}}{2*-1}=\frac{-45+\sqrt{2045}}{-2} $
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