-1/7y+y=18

Solution for -1/7y+y=18 equation:

-1/7y+y=18

We move all terms to the left:

-1/7y+y-(18)=0


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R


We add all the numbers together, and all the variables

y-1/7y-18=0

We multiply all the terms by the denominator


y*7y-18*7y-1=0

Wy multiply elements

7y^2-126y-1=0

a = 7; b = -126; c = -1;
Δ = b2-4ac
Δ = -1262-4·7·(-1)
Δ = 15904
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:

$\sqrt{\Delta}=\sqrt{15904}=\sqrt{16*994}=\sqrt{16}*\sqrt{994}=4\sqrt{994}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-4\sqrt{994}}{2*7}=\frac{126-4\sqrt{994}}{14}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+4\sqrt{994}}{2*7}=\frac{126+4\sqrt{994}}{14}
$