34y-5=-1+1/4y

Solution for 34y-5=-1+1/4y equation:

34y-5=-1+1/4y

We move all terms to the left:

34y-5-(-1+1/4y)=0


Domain of the equation: 4y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

34y-(1/4y-1)-5=0

We get rid of parentheses

34y-1/4y+1-5=0

We multiply all the terms by the denominator


34y*4y+1*4y-5*4y-1=0

Wy multiply elements

136y^2+4y-20y-1=0

We add all the numbers together, and all the variables

136y^2-16y-1=0

a = 136; b = -16; c = -1;
Δ = b2-4ac
Δ = -162-4·136·(-1)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-20\sqrt{2}}{2*136}=\frac{16-20\sqrt{2}}{272}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+20\sqrt{2}}{2*136}=\frac{16+20\sqrt{2}}{272}
$