150=-5(-5-3p)10p

Solution for 150=-5(-5-3p)10p equation:

150=-5(-5-3p)10p

We move all terms to the left:

150-(-5(-5-3p)10p)=0

We add all the numbers together, and all the variables

-(-5(-3p-5)10p)+150=0


We calculate terms in parentheses: -(-5(-3p-5)10p), so:

-5(-3p-5)10p

We multiply parentheses

150p^2+250p

Back to the equation:

-(150p^2+250p)


We get rid of parentheses

-150p^2-250p+150=0

a = -150; b = -250; c = +150;
Δ = b2-4ac
Δ = -2502-4·(-150)·150
Δ = 152500
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:

$\sqrt{\Delta}=\sqrt{152500}=\sqrt{2500*61}=\sqrt{2500}*\sqrt{61}=50\sqrt{61}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-250)-50\sqrt{61}}{2*-150}=\frac{250-50\sqrt{61}}{-300}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-250)+50\sqrt{61}}{2*-150}=\frac{250+50\sqrt{61}}{-300}
$