5/4y+y=505

Solution for 5/4y+y=505 equation:

5/4y+y=505

We move all terms to the left:

5/4y+y-(505)=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-505=0

We multiply all the terms by the denominator


y*4y-505*4y+5=0

Wy multiply elements

4y^2-2020y+5=0

a = 4; b = -2020; c = +5;
Δ = b2-4ac
Δ = -20202-4·4·5
Δ = 4080320
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:

$\sqrt{\Delta}=\sqrt{4080320}=\sqrt{64*63755}=\sqrt{64}*\sqrt{63755}=8\sqrt{63755}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2020)-8\sqrt{63755}}{2*4}=\frac{2020-8\sqrt{63755}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2020)+8\sqrt{63755}}{2*4}=\frac{2020+8\sqrt{63755}}{8}
$