8p^2=8p+13

Solution for 8p^2=8p+13 equation:

8p^2=8p+13

We move all terms to the left:

8p^2-(8p+13)=0

We get rid of parentheses

8p^2-8p-13=0

a = 8; b = -8; c = -13;
Δ = b2-4ac
Δ = -82-4·8·(-13)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{30}}{2*8}=\frac{8-4\sqrt{30}}{16}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{30}}{2*8}=\frac{8+4\sqrt{30}}{16}
$