p^2-11p+13=8-5p

Solution for p^2-11p+13=8-5p equation:

p^2-11p+13=8-5p

We move all terms to the left:

p^2-11p+13-(8-5p)=0

We add all the numbers together, and all the variables

p^2-11p-(-5p+8)+13=0

We get rid of parentheses

p^2-11p+5p-8+13=0

We add all the numbers together, and all the variables

p^2-6p+5=0

a = 1; b = -6; c = +5;
Δ = b2-4ac
Δ = -62-4·1·5
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4}{2*1}=\frac{2}{2}
=1
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4}{2*1}=\frac{10}{2}
=5
$