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8p^2+26p+15=12
We move all terms to the left:
8p^2+26p+15-(12)=0
We add all the numbers together, and all the variables
8p^2+26p+3=0
a = 8; b = 26; c = +3;
Δ = b2-4ac
Δ = 262-4·8·3
Δ = 580
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}$$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{145}}{2*8}=\frac{-26-2\sqrt{145}}{16} $$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{145}}{2*8}=\frac{-26+2\sqrt{145}}{16} $
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