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11-3p=2/3p
We move all terms to the left:
11-3p-(2/3p)=0
Domain of the equation: 3p)!=0We add all the numbers together, and all the variables
p!=0/1
p!=0
p∈R
-3p-(+2/3p)+11=0
We get rid of parentheses
-3p-2/3p+11=0
We multiply all the terms by the denominator
-3p*3p+11*3p-2=0
Wy multiply elements
-9p^2+33p-2=0
a = -9; b = 33; c = -2;
Δ = b2-4ac
Δ = 332-4·(-9)·(-2)
Δ = 1017
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-3\sqrt{113}}{2*-9}=\frac{-33-3\sqrt{113}}{-18} $$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+3\sqrt{113}}{2*-9}=\frac{-33+3\sqrt{113}}{-18} $
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