p(4-5p)=-5

Solution for p(4-5p)=-5 equation:

p(4-5p)=-5

We move all terms to the left:

p(4-5p)-(-5)=0

We add all the numbers together, and all the variables

p(-5p+4)-(-5)=0

We add all the numbers together, and all the variables

p(-5p+4)+5=0

We multiply parentheses

-5p^2+4p+5=0

a = -5; b = 4; c = +5;
Δ = b2-4ac
Δ = 42-4·(-5)·5
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{29}}{2*-5}=\frac{-4-2\sqrt{29}}{-10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{29}}{2*-5}=\frac{-4+2\sqrt{29}}{-10}
$