(51/2)r=110

Solution for (51/2)r=110 equation:

(51/2)r=110

We move all terms to the left:

(51/2)r-(110)=0


Domain of the equation: 2)r!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

(+51/2)r-110=0

We multiply parentheses

51r^2-110=0

a = 51; b = 0; c = -110;
Δ = b2-4ac
Δ = 02-4·51·(-110)
Δ = 22440
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:

$\sqrt{\Delta}=\sqrt{22440}=\sqrt{4*5610}=\sqrt{4}*\sqrt{5610}=2\sqrt{5610}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{5610}}{2*51}=\frac{0-2\sqrt{5610}}{102}
=-\frac{2\sqrt{5610}}{102}
=-\frac{\sqrt{5610}}{51}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{5610}}{2*51}=\frac{0+2\sqrt{5610}}{102}
=\frac{2\sqrt{5610}}{102}
=\frac{\sqrt{5610}}{51}
$