5/4y+y=189

Solution for 5/4y+y=189 equation:

5/4y+y=189

We move all terms to the left:

5/4y+y-(189)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We add all the numbers together, and all the variables

y+5/4y-189=0

We multiply all the terms by the denominator


y*4y-189*4y+5=0

Wy multiply elements

4y^2-756y+5=0

a = 4; b = -756; c = +5;
Δ = b2-4ac
Δ = -7562-4·4·5
Δ = 571456
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:

$\sqrt{\Delta}=\sqrt{571456}=\sqrt{64*8929}=\sqrt{64}*\sqrt{8929}=8\sqrt{8929}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-756)-8\sqrt{8929}}{2*4}=\frac{756-8\sqrt{8929}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-756)+8\sqrt{8929}}{2*4}=\frac{756+8\sqrt{8929}}{8}
$