1/6y+7=6y-6

Solution for 1/6y+7=6y-6 equation:

1/6y+7=6y-6

We move all terms to the left:

1/6y+7-(6y-6)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We get rid of parentheses

1/6y-6y+6+7=0

We multiply all the terms by the denominator


-6y*6y+6*6y+7*6y+1=0

Wy multiply elements

-36y^2+36y+42y+1=0

We add all the numbers together, and all the variables

-36y^2+78y+1=0

a = -36; b = 78; c = +1;
Δ = b2-4ac
Δ = 782-4·(-36)·1
Δ = 6228
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:

$\sqrt{\Delta}=\sqrt{6228}=\sqrt{36*173}=\sqrt{36}*\sqrt{173}=6\sqrt{173}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-6\sqrt{173}}{2*-36}=\frac{-78-6\sqrt{173}}{-72}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+6\sqrt{173}}{2*-36}=\frac{-78+6\sqrt{173}}{-72}
$