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29p^2+91p-214=-4+8p
We move all terms to the left:
29p^2+91p-214-(-4+8p)=0
We add all the numbers together, and all the variables
29p^2+91p-(8p-4)-214=0
We get rid of parentheses
29p^2+91p-8p+4-214=0
We add all the numbers together, and all the variables
29p^2+83p-210=0
a = 29; b = 83; c = -210;
Δ = b2-4ac
Δ = 832-4·29·(-210)
Δ = 31249
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{-(83)-\sqrt{31249}}{2*29}=\frac{-83-\sqrt{31249}}{58} $$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(83)+\sqrt{31249}}{2*29}=\frac{-83+\sqrt{31249}}{58} $
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