80p+700=75p^2+10p+200

Solution for 80p+700=75p^2+10p+200 equation:

80p+700=75p^2+10p+200

We move all terms to the left:

80p+700-(75p^2+10p+200)=0

We get rid of parentheses

-75p^2+80p-10p-200+700=0

We add all the numbers together, and all the variables

-75p^2+70p+500=0

a = -75; b = 70; c = +500;
Δ = b2-4ac
Δ = 702-4·(-75)·500
Δ = 154900
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:

$\sqrt{\Delta}=\sqrt{154900}=\sqrt{100*1549}=\sqrt{100}*\sqrt{1549}=10\sqrt{1549}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-10\sqrt{1549}}{2*-75}=\frac{-70-10\sqrt{1549}}{-150}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+10\sqrt{1549}}{2*-75}=\frac{-70+10\sqrt{1549}}{-150}
$