1/6y+y=210

Solution for 1/6y+y=210 equation:

1/6y+y=210

We move all terms to the left:

1/6y+y-(210)=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-210=0

We multiply all the terms by the denominator


y*6y-210*6y+1=0

Wy multiply elements

6y^2-1260y+1=0

a = 6; b = -1260; c = +1;
Δ = b2-4ac
Δ = -12602-4·6·1
Δ = 1587576
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:

$\sqrt{\Delta}=\sqrt{1587576}=\sqrt{4*396894}=\sqrt{4}*\sqrt{396894}=2\sqrt{396894}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1260)-2\sqrt{396894}}{2*6}=\frac{1260-2\sqrt{396894}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1260)+2\sqrt{396894}}{2*6}=\frac{1260+2\sqrt{396894}}{12}
$