3p-5=-8(6+5p)p=

Solution for 3p-5=-8(6+5p)p= equation:

3p-5=-8(6+5p)p=

We move all terms to the left:

3p-5-(-8(6+5p)p)=0

We add all the numbers together, and all the variables

3p-(-8(5p+6)p)-5=0


We calculate terms in parentheses: -(-8(5p+6)p), so:

-8(5p+6)p

We multiply parentheses

-40p^2-48p

Back to the equation:

-(-40p^2-48p)


We get rid of parentheses

40p^2+48p+3p-5=0

We add all the numbers together, and all the variables

40p^2+51p-5=0

a = 40; b = 51; c = -5;
Δ = b2-4ac
Δ = 512-4·40·(-5)
Δ = 3401
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{-(51)-\sqrt{3401}}{2*40}=\frac{-51-\sqrt{3401}}{80}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+\sqrt{3401}}{2*40}=\frac{-51+\sqrt{3401}}{80}
$