42/y=1.09*y

Solution for 42/y=1.09*y equation:

42/y=1.09y

We move all terms to the left:

42/y-(1.09y)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

42/y-(+1.09y)=0

We get rid of parentheses

42/y-1.09y=0

We multiply all the terms by the denominator


-(1.09y)*y+42=0

We add all the numbers together, and all the variables

-(+1.09y)*y+42=0

We multiply parentheses

-y^2+42=0

We add all the numbers together, and all the variables

-1y^2+42=0

a = -1; b = 0; c = +42;
Δ = b2-4ac
Δ = 02-4·(-1)·42
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{42}}{2*-1}=\frac{0-2\sqrt{42}}{-2}
=-\frac{2\sqrt{42}}{-2}
=-\frac{\sqrt{42}}{-1}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{42}}{2*-1}=\frac{0+2\sqrt{42}}{-2}
=\frac{2\sqrt{42}}{-2}
=\frac{\sqrt{42}}{-1}
$