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5/2p-2/7p+12=6
We move all terms to the left:
5/2p-2/7p+12-(6)=0
Domain of the equation: 2p!=0
p!=0/2
p!=0
p∈R
Domain of the equation: 7p!=0We add all the numbers together, and all the variables
p!=0/7
p!=0
p∈R
5/2p-2/7p+6=0
We calculate fractions
35p/14p^2+(-4p)/14p^2+6=0
We multiply all the terms by the denominator
35p+(-4p)+6*14p^2=0
Wy multiply elements
84p^2+35p+(-4p)=0
We get rid of parentheses
84p^2+35p-4p=0
We add all the numbers together, and all the variables
84p^2+31p=0
a = 84; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·84·0
Δ = 961
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{961}=31$$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*84}=\frac{-62}{168} =-31/84 $$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*84}=\frac{0}{168} =0 $
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