r=(56-r)^(1/2)

Solution for r=(56-r)^(1/2) equation:

r=(56-r)^(1/2)

We move all terms to the left:

r-((56-r)^(1/2))=0

We add all the numbers together, and all the variables

r-((-1r+56)^(+1/2))=0

We multiply all the terms by the denominator


r*2))-((-1r+1+56)^(=0

We add all the numbers together, and all the variables

r*2))-((-1r+57)^(=0

We add all the numbers together, and all the variables

-1r+r*2))-((=0

Wy multiply elements

2r^2-1r=0

a = 2; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·2·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*2}=\frac{0}{4}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*2}=\frac{2}{4}
=1/2
$