8-13p=6p(6-p)

Solution for 8-13p=6p(6-p) equation:

8-13p=6p(6-p)

We move all terms to the left:

8-13p-(6p(6-p))=0

We add all the numbers together, and all the variables

-13p-(6p(-1p+6))+8=0


We calculate terms in parentheses: -(6p(-1p+6)), so:

6p(-1p+6)

We multiply parentheses

-6p^2+36p

Back to the equation:

-(-6p^2+36p)


We get rid of parentheses

6p^2-36p-13p+8=0

We add all the numbers together, and all the variables

6p^2-49p+8=0

a = 6; b = -49; c = +8;
Δ = b2-4ac
Δ = -492-4·6·8
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-47}{2*6}=\frac{2}{12}
=1/6
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+47}{2*6}=\frac{96}{12}
=8
$