-7+0.5y+11+1/6y=9

Solution for -7+0.5y+11+1/6y=9 equation:

-7+0.5y+11+1/6y=9

We move all terms to the left:

-7+0.5y+11+1/6y-(9)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We add all the numbers together, and all the variables

0.5y+1/6y-5=0

We multiply all the terms by the denominator


(0.5y)*6y-5*6y+1=0

We add all the numbers together, and all the variables

(+0.5y)*6y-5*6y+1=0

We multiply parentheses

0y^2-5*6y+1=0

Wy multiply elements

0y^2-30y+1=0

We add all the numbers together, and all the variables

y^2-30y+1=0

a = 1; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·1·1
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-8\sqrt{14}}{2*1}=\frac{30-8\sqrt{14}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+8\sqrt{14}}{2*1}=\frac{30+8\sqrt{14}}{2}
$