-8p^2+13=-9p+9

Solution for -8p^2+13=-9p+9 equation:

-8p^2+13=-9p+9

We move all terms to the left:

-8p^2+13-(-9p+9)=0

We get rid of parentheses

-8p^2+9p-9+13=0

We add all the numbers together, and all the variables

-8p^2+9p+4=0

a = -8; b = 9; c = +4;
Δ = b2-4ac
Δ = 92-4·(-8)·4
Δ = 209
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{-(9)-\sqrt{209}}{2*-8}=\frac{-9-\sqrt{209}}{-16}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{209}}{2*-8}=\frac{-9+\sqrt{209}}{-16}
$