(1/4)r+1=32

Solution for (1/4)r+1=32 equation:

(1/4)r+1=32

We move all terms to the left:

(1/4)r+1-(32)=0


Domain of the equation: 4)r!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

(+1/4)r+1-32=0

We add all the numbers together, and all the variables

(+1/4)r-31=0

We multiply parentheses

r^2-31=0

a = 1; b = 0; c = -31;
Δ = b2-4ac
Δ = 02-4·1·(-31)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{31}}{2*1}=\frac{0-2\sqrt{31}}{2}
=-\frac{2\sqrt{31}}{2}
=-\sqrt{31}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{31}}{2*1}=\frac{0+2\sqrt{31}}{2}
=\frac{2\sqrt{31}}{2}
=\sqrt{31}
$