1000=(150-5p)p

Solution for 1000=(150-5p)p equation:

1000=(150-5p)p

We move all terms to the left:

1000-((150-5p)p)=0

We add all the numbers together, and all the variables

-((-5p+150)p)+1000=0


We calculate terms in parentheses: -((-5p+150)p), so:

(-5p+150)p

We multiply parentheses

-5p^2+150p

Back to the equation:

-(-5p^2+150p)


We get rid of parentheses

5p^2-150p+1000=0

a = 5; b = -150; c = +1000;
Δ = b2-4ac
Δ = -1502-4·5·1000
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-50}{2*5}=\frac{100}{10}
=10
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+50}{2*5}=\frac{200}{10}
=20
$