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(2p+1)(3p+4)=225
We move all terms to the left:
(2p+1)(3p+4)-(225)=0
We multiply parentheses ..
(+6p^2+8p+3p+4)-225=0
We get rid of parentheses
6p^2+8p+3p+4-225=0
We add all the numbers together, and all the variables
6p^2+11p-221=0
a = 6; b = 11; c = -221;
Δ = b2-4ac
Δ = 112-4·6·(-221)
Δ = 5425
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}$$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5425}=\sqrt{25*217}=\sqrt{25}*\sqrt{217}=5\sqrt{217}$$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-5\sqrt{217}}{2*6}=\frac{-11-5\sqrt{217}}{12} $$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+5\sqrt{217}}{2*6}=\frac{-11+5\sqrt{217}}{12} $
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