-17-2r=4-3(r+8)r=

Solution for -17-2r=4-3(r+8)r= equation:

-17-2r=4-3(r+8)r=

We move all terms to the left:

-17-2r-(4-3(r+8)r)=0


We calculate terms in parentheses: -(4-3(r+8)r), so:

4-3(r+8)r

determiningTheFunctionDomain
-3(r+8)r+4

We multiply parentheses

-3r^2-24r+4

Back to the equation:

-(-3r^2-24r+4)


We get rid of parentheses

3r^2+24r-2r-4-17=0

We add all the numbers together, and all the variables

3r^2+22r-21=0

a = 3; b = 22; c = -21;
Δ = b2-4ac
Δ = 222-4·3·(-21)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-4\sqrt{46}}{2*3}=\frac{-22-4\sqrt{46}}{6}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+4\sqrt{46}}{2*3}=\frac{-22+4\sqrt{46}}{6}
$