1/6y+y=25

Solution for 1/6y+y=25 equation:

1/6y+y=25

We move all terms to the left:

1/6y+y-(25)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We add all the numbers together, and all the variables

y+1/6y-25=0

We multiply all the terms by the denominator


y*6y-25*6y+1=0

Wy multiply elements

6y^2-150y+1=0

a = 6; b = -150; c = +1;
Δ = b2-4ac
Δ = -1502-4·6·1
Δ = 22476
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:

$\sqrt{\Delta}=\sqrt{22476}=\sqrt{4*5619}=\sqrt{4}*\sqrt{5619}=2\sqrt{5619}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-2\sqrt{5619}}{2*6}=\frac{150-2\sqrt{5619}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+2\sqrt{5619}}{2*6}=\frac{150+2\sqrt{5619}}{12}
$