-9.75y=1/4y-4

Solution for -9.75y=1/4y-4 equation:

-9.75y=1/4y-4

We move all terms to the left:

-9.75y-(1/4y-4)=0


Domain of the equation: 4y-4)!=0

y∈R


We get rid of parentheses

-9.75y-1/4y+4=0

We multiply all the terms by the denominator


-(9.75y)*4y+4*4y-1=0

We add all the numbers together, and all the variables

-(+9.75y)*4y+4*4y-1=0

We multiply parentheses

-36y^2+4*4y-1=0

Wy multiply elements

-36y^2+16y-1=0

a = -36; b = 16; c = -1;
Δ = b2-4ac
Δ = 162-4·(-36)·(-1)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{7}}{2*-36}=\frac{-16-4\sqrt{7}}{-72}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{7}}{2*-36}=\frac{-16+4\sqrt{7}}{-72}
$