29p2+91p-214=-4+8p2

Solution for 29p2+91p-214=-4+8p2 equation:

29p^2+91p-214=-4+8p^2

We move all terms to the left:

29p^2+91p-214-(-4+8p^2)=0

We get rid of parentheses

29p^2-8p^2+91p+4-214=0

We add all the numbers together, and all the variables

21p^2+91p-210=0

a = 21; b = 91; c = -210;
Δ = b2-4ac
Δ = 912-4·21·(-210)
Δ = 25921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25921}=161$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(91)-161}{2*21}=\frac{-252}{42}
=-6
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(91)+161}{2*21}=\frac{70}{42}
=1+2/3
$