80x-(2x^2)+300-(x^2)=0

Solution for 80x-(2x^2)+300-(x^2)=0 equation:

80x-(2x^2)+300-(x^2)=0

determiningTheFunctionDomain
-2x^2-x^2+80x+300=0

We add all the numbers together, and all the variables

-3x^2+80x+300=0

a = -3; b = 80; c = +300;
Δ = b2-4ac
Δ = 802-4·(-3)·300
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-100}{2*-3}=\frac{-180}{-6}
=+30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+100}{2*-3}=\frac{20}{-6}
=-3+1/3
$