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15-1/5r=2r-1
We move all terms to the left:
15-1/5r-(2r-1)=0
Domain of the equation: 5r!=0We get rid of parentheses
r!=0/5
r!=0
r∈R
-1/5r-2r+1+15=0
We multiply all the terms by the denominator
-2r*5r+1*5r+15*5r-1=0
Wy multiply elements
-10r^2+5r+75r-1=0
We add all the numbers together, and all the variables
-10r^2+80r-1=0
a = -10; b = 80; c = -1;
Δ = b2-4ac
Δ = 802-4·(-10)·(-1)
Δ = 6360
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}$$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6360}=\sqrt{4*1590}=\sqrt{4}*\sqrt{1590}=2\sqrt{1590}$$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-2\sqrt{1590}}{2*-10}=\frac{-80-2\sqrt{1590}}{-20} $$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+2\sqrt{1590}}{2*-10}=\frac{-80+2\sqrt{1590}}{-20} $
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