5p^2+1=8p

Solution for 5p^2+1=8p equation:

5p^2+1=8p

We move all terms to the left:

5p^2+1-(8p)=0

a = 5; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·5·1
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{11}}{2*5}=\frac{8-2\sqrt{11}}{10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{11}}{2*5}=\frac{8+2\sqrt{11}}{10}
$