66/22r-16/16-1=r+8

Solution for 66/22r-16/16-1=r+8 equation:

66/22r-16/16-1=r+8

We move all terms to the left:

66/22r-16/16-1-(r+8)=0


Domain of the equation: 22r!=0

r!=0/22

r!=0

r∈R


We add all the numbers together, and all the variables

66/22r-(r+8)-2=0

We get rid of parentheses

66/22r-r-8-2=0

We multiply all the terms by the denominator


-r*22r-8*22r-2*22r+66=0

Wy multiply elements

-22r^2-176r-44r+66=0

We add all the numbers together, and all the variables

-22r^2-220r+66=0

a = -22; b = -220; c = +66;
Δ = b2-4ac
Δ = -2202-4·(-22)·66
Δ = 54208
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{54208}=\sqrt{7744*7}=\sqrt{7744}*\sqrt{7}=88\sqrt{7}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-220)-88\sqrt{7}}{2*-22}=\frac{220-88\sqrt{7}}{-44}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-220)+88\sqrt{7}}{2*-22}=\frac{220+88\sqrt{7}}{-44}
$