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10=3p^2-5p-8
We move all terms to the left:
10-(3p^2-5p-8)=0
We get rid of parentheses
-3p^2+5p+8+10=0
We add all the numbers together, and all the variables
-3p^2+5p+18=0
a = -3; b = 5; c = +18;
Δ = b2-4ac
Δ = 52-4·(-3)·18
Δ = 241
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{-(5)-\sqrt{241}}{2*-3}=\frac{-5-\sqrt{241}}{-6} $$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{241}}{2*-3}=\frac{-5+\sqrt{241}}{-6} $
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