P(8)=5x^2-6*8+1

Solution for P(8)=5x^2-6*8+1 equation:

(8)=5P^2-6*8+1

We move all terms to the left:

(8)-(5P^2-6*8+1)=0

We get rid of parentheses

-5P^2-1+8+6*8=0

We add all the numbers together, and all the variables

-5P^2+55=0

a = -5; b = 0; c = +55;
Δ = b2-4ac
Δ = 02-4·(-5)·55
Δ = 1100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1100}=\sqrt{100*11}=\sqrt{100}*\sqrt{11}=10\sqrt{11}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{11}}{2*-5}=\frac{0-10\sqrt{11}}{-10}
=-\frac{10\sqrt{11}}{-10}
=-\frac{\sqrt{11}}{-1}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{11}}{2*-5}=\frac{0+10\sqrt{11}}{-10}
=\frac{10\sqrt{11}}{-10}
=\frac{\sqrt{11}}{-1}
$