1/6y+8=7y-33

Solution for 1/6y+8=7y-33 equation:

1/6y+8=7y-33

We move all terms to the left:

1/6y+8-(7y-33)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We get rid of parentheses

1/6y-7y+33+8=0

We multiply all the terms by the denominator


-7y*6y+33*6y+8*6y+1=0

Wy multiply elements

-42y^2+198y+48y+1=0

We add all the numbers together, and all the variables

-42y^2+246y+1=0

a = -42; b = 246; c = +1;
Δ = b2-4ac
Δ = 2462-4·(-42)·1
Δ = 60684
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:

$\sqrt{\Delta}=\sqrt{60684}=\sqrt{4*15171}=\sqrt{4}*\sqrt{15171}=2\sqrt{15171}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(246)-2\sqrt{15171}}{2*-42}=\frac{-246-2\sqrt{15171}}{-84}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(246)+2\sqrt{15171}}{2*-42}=\frac{-246+2\sqrt{15171}}{-84}
$