y-6/7y=22

Solution for y-6/7y=22 equation:

y-6/7y=22

We move all terms to the left:

y-6/7y-(22)=0


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R


We multiply all the terms by the denominator


y*7y-22*7y-6=0

Wy multiply elements

7y^2-154y-6=0

a = 7; b = -154; c = -6;
Δ = b2-4ac
Δ = -1542-4·7·(-6)
Δ = 23884
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:

$\sqrt{\Delta}=\sqrt{23884}=\sqrt{4*5971}=\sqrt{4}*\sqrt{5971}=2\sqrt{5971}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-154)-2\sqrt{5971}}{2*7}=\frac{154-2\sqrt{5971}}{14}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-154)+2\sqrt{5971}}{2*7}=\frac{154+2\sqrt{5971}}{14}
$