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(1/2)(2p+9)=-p+5
We move all terms to the left:
(1/2)(2p+9)-(-p+5)=0
Domain of the equation: 2)(2p+9)!=0We add all the numbers together, and all the variables
p∈R
(+1/2)(2p+9)-(-1p+5)=0
We get rid of parentheses
(+1/2)(2p+9)+1p-5=0
We multiply parentheses ..
(+2p^2+1/2*9)+1p-5=0
We multiply all the terms by the denominator
(+2p^2+1+1p*2*9)-5*2*9)=0
We add all the numbers together, and all the variables
(+2p^2+1+1p*2*9)=0
We get rid of parentheses
2p^2+1p*2*9+1=0
Wy multiply elements
2p^2+18p*9+1=0
Wy multiply elements
2p^2+162p+1=0
a = 2; b = 162; c = +1;
Δ = b2-4ac
Δ = 1622-4·2·1
Δ = 26236
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}$$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{26236}=\sqrt{4*6559}=\sqrt{4}*\sqrt{6559}=2\sqrt{6559}$$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(162)-2\sqrt{6559}}{2*2}=\frac{-162-2\sqrt{6559}}{4} $$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(162)+2\sqrt{6559}}{2*2}=\frac{-162+2\sqrt{6559}}{4} $
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