2y-5=1/4y+9

Solution for 2y-5=1/4y+9 equation:

2y-5=1/4y+9

We move all terms to the left:

2y-5-(1/4y+9)=0


Domain of the equation: 4y+9)!=0

y∈R


We get rid of parentheses

2y-1/4y-9-5=0

We multiply all the terms by the denominator


2y*4y-9*4y-5*4y-1=0

Wy multiply elements

8y^2-36y-20y-1=0

We add all the numbers together, and all the variables

8y^2-56y-1=0

a = 8; b = -56; c = -1;
Δ = b2-4ac
Δ = -562-4·8·(-1)
Δ = 3168
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:

$\sqrt{\Delta}=\sqrt{3168}=\sqrt{144*22}=\sqrt{144}*\sqrt{22}=12\sqrt{22}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-12\sqrt{22}}{2*8}=\frac{56-12\sqrt{22}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+12\sqrt{22}}{2*8}=\frac{56+12\sqrt{22}}{16}
$