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5/8p+6=2/3p-1
We move all terms to the left:
5/8p+6-(2/3p-1)=0
Domain of the equation: 8p!=0
p!=0/8
p!=0
p∈R
Domain of the equation: 3p-1)!=0We get rid of parentheses
p∈R
5/8p-2/3p+1+6=0
We calculate fractions
15p/24p^2+(-16p)/24p^2+1+6=0
We add all the numbers together, and all the variables
15p/24p^2+(-16p)/24p^2+7=0
We multiply all the terms by the denominator
15p+(-16p)+7*24p^2=0
Wy multiply elements
168p^2+15p+(-16p)=0
We get rid of parentheses
168p^2+15p-16p=0
We add all the numbers together, and all the variables
168p^2-1p=0
a = 168; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·168·0
Δ = 1
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}$$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{1}=1$$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*168}=\frac{0}{336} =0 $$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*168}=\frac{2}{336} =1/168 $
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