-5-r=1/2r

Solution for -5-r=1/2r equation:

-5-r=1/2r

We move all terms to the left:

-5-r-(1/2r)=0


Domain of the equation: 2r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

-r-(+1/2r)-5=0

We add all the numbers together, and all the variables

-1r-(+1/2r)-5=0

We get rid of parentheses

-1r-1/2r-5=0

We multiply all the terms by the denominator


-1r*2r-5*2r-1=0

Wy multiply elements

-2r^2-10r-1=0

a = -2; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·(-2)·(-1)
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{23}}{2*-2}=\frac{10-2\sqrt{23}}{-4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{23}}{2*-2}=\frac{10+2\sqrt{23}}{-4}
$