.75y-5=-1+1/4y

Solution for .75y-5=-1+1/4y equation:

.75y-5=-1+1/4y

We move all terms to the left:

.75y-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

.75y-(1/4y-1)-5=0

We get rid of parentheses

.75y-1/4y+1-5=0

We multiply all the terms by the denominator


(.75y)*4y+1*4y-5*4y-1=0

We add all the numbers together, and all the variables

(+.75y)*4y+1*4y-5*4y-1=0

We multiply parentheses

4y^2+1*4y-5*4y-1=0

Wy multiply elements

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

We add all the numbers together, and all the variables

4y^2-16y-1=0

a = 4; b = -16; c = -1;
Δ = b2-4ac
Δ = -162-4·4·(-1)
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{17}}{2*4}=\frac{16-4\sqrt{17}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{17}}{2*4}=\frac{16+4\sqrt{17}}{8}
$