8p^2=13-12p

Solution for 8p^2=13-12p equation:

8p^2=13-12p

We move all terms to the left:

8p^2-(13-12p)=0

We add all the numbers together, and all the variables

8p^2-(-12p+13)=0

We get rid of parentheses

8p^2+12p-13=0

a = 8; b = 12; c = -13;
Δ = b2-4ac
Δ = 122-4·8·(-13)
Δ = 560
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:

$\sqrt{\Delta}=\sqrt{560}=\sqrt{16*35}=\sqrt{16}*\sqrt{35}=4\sqrt{35}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{35}}{2*8}=\frac{-12-4\sqrt{35}}{16}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{35}}{2*8}=\frac{-12+4\sqrt{35}}{16}
$