180x-x^2-6500=0

Solution for 180x-x^2-6500=0 equation:

180x-x^2-6500=0

We add all the numbers together, and all the variables

-1x^2+180x-6500=0

a = -1; b = 180; c = -6500;
Δ = b2-4ac
Δ = 1802-4·(-1)·(-6500)
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-80}{2*-1}=\frac{-260}{-2}
=+130
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+80}{2*-1}=\frac{-100}{-2}
=+50
$