y-6/7y=14

Solution for y-6/7y=14 equation:

y-6/7y=14

We move all terms to the left:

y-6/7y-(14)=0


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R


We multiply all the terms by the denominator


y*7y-14*7y-6=0

Wy multiply elements

7y^2-98y-6=0

a = 7; b = -98; c = -6;
Δ = b2-4ac
Δ = -982-4·7·(-6)
Δ = 9772
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:

$\sqrt{\Delta}=\sqrt{9772}=\sqrt{4*2443}=\sqrt{4}*\sqrt{2443}=2\sqrt{2443}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-98)-2\sqrt{2443}}{2*7}=\frac{98-2\sqrt{2443}}{14}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-98)+2\sqrt{2443}}{2*7}=\frac{98+2\sqrt{2443}}{14}
$