1/4y+y+5/4y=50

Solution for 1/4y+y+5/4y=50 equation:

1/4y+y+5/4y=50

We move all terms to the left:

1/4y+y+5/4y-(50)=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+1/4y+5/4y-50=0

We multiply all the terms by the denominator


y*4y-50*4y+1+5=0

We add all the numbers together, and all the variables

y*4y-50*4y+6=0

Wy multiply elements

4y^2-200y+6=0

a = 4; b = -200; c = +6;
Δ = b2-4ac
Δ = -2002-4·4·6
Δ = 39904
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:

$\sqrt{\Delta}=\sqrt{39904}=\sqrt{16*2494}=\sqrt{16}*\sqrt{2494}=4\sqrt{2494}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-4\sqrt{2494}}{2*4}=\frac{200-4\sqrt{2494}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+4\sqrt{2494}}{2*4}=\frac{200+4\sqrt{2494}}{8}
$