1/2r=r-15

Solution for 1/2r=r-15 equation:

1/2r=r-15

We move all terms to the left:

1/2r-(r-15)=0


Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R


We get rid of parentheses

1/2r-r+15=0

We multiply all the terms by the denominator


-r*2r+15*2r+1=0

Wy multiply elements

-2r^2+30r+1=0

a = -2; b = 30; c = +1;
Δ = b2-4ac
Δ = 302-4·(-2)·1
Δ = 908
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:

$\sqrt{\Delta}=\sqrt{908}=\sqrt{4*227}=\sqrt{4}*\sqrt{227}=2\sqrt{227}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{227}}{2*-2}=\frac{-30-2\sqrt{227}}{-4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{227}}{2*-2}=\frac{-30+2\sqrt{227}}{-4}
$