-9(r)=2/3r-6

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Solution for -9(r)=2/3r-6 equation:



-9(r)=2/3r-6
We move all terms to the left:
-9(r)-(2/3r-6)=0
Domain of the equation: 3r-6)!=0
r∈R
We get rid of parentheses
-9r-2/3r+6=0
We multiply all the terms by the denominator
-9r*3r+6*3r-2=0
Wy multiply elements
-27r^2+18r-2=0
a = -27; b = 18; c = -2;
Δ = b2-4ac
Δ = 182-4·(-27)·(-2)
Δ = 108
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:
$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{3}}{2*-27}=\frac{-18-6\sqrt{3}}{-54} $
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{3}}{2*-27}=\frac{-18+6\sqrt{3}}{-54} $

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