P(t)=4t^2+2t-1

Solution for P(t)=4t^2+2t-1 equation:

(P)=4P^2+2P-1

We move all terms to the left:

(P)-(4P^2+2P-1)=0

We get rid of parentheses

-4P^2+P-2P+1=0

We add all the numbers together, and all the variables

-4P^2-1P+1=0

a = -4; b = -1; c = +1;
Δ = b2-4ac
Δ = -12-4·(-4)·1
Δ = 17
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{-(-1)-\sqrt{17}}{2*-4}=\frac{1-\sqrt{17}}{-8}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{17}}{2*-4}=\frac{1+\sqrt{17}}{-8}
$