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8.12p+6.83p+5.05=16.7p^2+6.83p
We move all terms to the left:
8.12p+6.83p+5.05-(16.7p^2+6.83p)=0
We add all the numbers together, and all the variables
14.95p-(16.7p^2+6.83p)+5.05=0
We get rid of parentheses
-16.7p^2+14.95p-6.83p+5.05=0
We add all the numbers together, and all the variables
-16.7p^2+8.12p+5.05=0
a = -16.7; b = 8.12; c = +5.05;
Δ = b2-4ac
Δ = 8.122-4·(-16.7)·5.05
Δ = 403.2744
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}$$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8.12)-\sqrt{403.2744}}{2*-16.7}=\frac{-8.12-\sqrt{403.2744}}{-33.4} $$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8.12)+\sqrt{403.2744}}{2*-16.7}=\frac{-8.12+\sqrt{403.2744}}{-33.4} $
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