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7-1/2p=3p
We move all terms to the left:
7-1/2p-(3p)=0
Domain of the equation: 2p!=0We add all the numbers together, and all the variables
p!=0/2
p!=0
p∈R
-3p-1/2p+7=0
We multiply all the terms by the denominator
-3p*2p+7*2p-1=0
Wy multiply elements
-6p^2+14p-1=0
a = -6; b = 14; c = -1;
Δ = b2-4ac
Δ = 142-4·(-6)·(-1)
Δ = 172
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}$$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{43}}{2*-6}=\frac{-14-2\sqrt{43}}{-12} $$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{43}}{2*-6}=\frac{-14+2\sqrt{43}}{-12} $
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