1/4y+y=27,6

Solution for 1/4y+y=27,6 equation:

1/4y+y=27.6

We move all terms to the left:

1/4y+y-(27.6)=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-27.6=0

We multiply all the terms by the denominator


y*4y-(27.6)*4y+1=0

We multiply parentheses

y*4y-110.4y+1=0

Wy multiply elements

4y^2-110.4y+1=0

a = 4; b = -110.4; c = +1;
Δ = b2-4ac
Δ = -110.42-4·4·1
Δ = 12172.16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110.4)-\sqrt{12172.16}}{2*4}=\frac{110.4-\sqrt{12172.16}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110.4)+\sqrt{12172.16}}{2*4}=\frac{110.4+\sqrt{12172.16}}{8}
$