300+100p=315+5p*p

Solution for 300+100p=315+5p*p equation:

300+100p=315+5p*p

We move all terms to the left:

300+100p-(315+5p*p)=0

We add all the numbers together, and all the variables

100p-(5p*p+315)+300=0

We get rid of parentheses

100p-5p*p-315+300=0

We add all the numbers together, and all the variables

100p-5p*p-15=0

Wy multiply elements

-5p^2+100p-15=0

a = -5; b = 100; c = -15;
Δ = b2-4ac
Δ = 1002-4·(-5)·(-15)
Δ = 9700
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:

$\sqrt{\Delta}=\sqrt{9700}=\sqrt{100*97}=\sqrt{100}*\sqrt{97}=10\sqrt{97}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-10\sqrt{97}}{2*-5}=\frac{-100-10\sqrt{97}}{-10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+10\sqrt{97}}{2*-5}=\frac{-100+10\sqrt{97}}{-10}
$