y=101/6X

Solution for y=101/6X equation:

y=101/6y

We move all terms to the left:

y-(101/6y)=0


Domain of the equation: 6y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

y-(+101/6y)=0

We get rid of parentheses

y-101/6y=0

We multiply all the terms by the denominator


y*6y-101=0

Wy multiply elements

6y^2-101=0

a = 6; b = 0; c = -101;
Δ = b2-4ac
Δ = 02-4·6·(-101)
Δ = 2424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2424}=\sqrt{4*606}=\sqrt{4}*\sqrt{606}=2\sqrt{606}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{606}}{2*6}=\frac{0-2\sqrt{606}}{12}
=-\frac{2\sqrt{606}}{12}
=-\frac{\sqrt{606}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{606}}{2*6}=\frac{0+2\sqrt{606}}{12}
=\frac{2\sqrt{606}}{12}
=\frac{\sqrt{606}}{6}
$