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

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

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

We move all terms to the left:

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

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

We add all the numbers together, and all the variables

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

a = -2; b = 80; c = +300;
Δ = b2-4ac
Δ = 802-4·(-2)·300
Δ = 8800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8800}=\sqrt{400*22}=\sqrt{400}*\sqrt{22}=20\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-20\sqrt{22}}{2*-2}=\frac{-80-20\sqrt{22}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+20\sqrt{22}}{2*-2}=\frac{-80+20\sqrt{22}}{-4}
$