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2p+3/3p-7=0
Domain of the equation: 3p!=0We multiply all the terms by the denominator
p!=0/3
p!=0
p∈R
2p*3p-7*3p+3=0
Wy multiply elements
6p^2-21p+3=0
a = 6; b = -21; c = +3;
Δ = b2-4ac
Δ = -212-4·6·3
Δ = 369
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}$$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{41}}{2*6}=\frac{21-3\sqrt{41}}{12} $$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{41}}{2*6}=\frac{21+3\sqrt{41}}{12} $
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