1/3*r=17

Solution for 1/3*r=17 equation:

1/3*r=17

We move all terms to the left:

1/3*r-(17)=0


Domain of the equation: 3*r!=0

r!=0/1

r!=0

r∈R


We multiply all the terms by the denominator


-17*3*r+1=0

Wy multiply elements

-51r*r+1=0

Wy multiply elements

-51r^2+1=0

a = -51; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-51)·1
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{51}}{2*-51}=\frac{0-2\sqrt{51}}{-102}
=-\frac{2\sqrt{51}}{-102}
=-\frac{\sqrt{51}}{-51}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{51}}{2*-51}=\frac{0+2\sqrt{51}}{-102}
=\frac{2\sqrt{51}}{-102}
=\frac{\sqrt{51}}{-51}
$