180x+19000=-2(x^2)+660x

Solution for 180x+19000=-2(x^2)+660x equation:

180x+19000=-2(x^2)+660x

We move all terms to the left:

180x+19000-(-2(x^2)+660x)=0

determiningTheFunctionDomain
-(-2x^2+660x)+180x+19000=0

We get rid of parentheses

2x^2-660x+180x+19000=0

We add all the numbers together, and all the variables

2x^2-480x+19000=0

a = 2; b = -480; c = +19000;
Δ = b2-4ac
Δ = -4802-4·2·19000
Δ = 78400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{78400}=280$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-480)-280}{2*2}=\frac{200}{4}
=50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-480)+280}{2*2}=\frac{760}{4}
=190
$