-0.5x^2+40x-300=450

Solution for -0.5x^2+40x-300=450 equation:

-0.5x^2+40x-300=450

We move all terms to the left:

-0.5x^2+40x-300-(450)=0

We add all the numbers together, and all the variables

-0.5x^2+40x-750=0

a = -0.5; b = 40; c = -750;
Δ = b2-4ac
Δ = 402-4·(-0.5)·(-750)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-10}{2*-0.5}=\frac{-50}{-1}
=+50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+10}{2*-0.5}=\frac{-30}{-1}
=+30
$