1/5y+y=6

Solution for 1/5y+y=6 equation:

1/5y+y=6

We move all terms to the left:

1/5y+y-(6)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

y+1/5y-6=0

We multiply all the terms by the denominator


y*5y-6*5y+1=0

Wy multiply elements

5y^2-30y+1=0

a = 5; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·5·1
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-4\sqrt{55}}{2*5}=\frac{30-4\sqrt{55}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+4\sqrt{55}}{2*5}=\frac{30+4\sqrt{55}}{10}
$