460-2x=20+0.5x^2

Solution for 460-2x=20+0.5x^2 equation:

460-2x=20+0.5x^2

We move all terms to the left:

460-2x-(20+0.5x^2)=0

We get rid of parentheses

-0.5x^2-2x-20+460=0

We add all the numbers together, and all the variables

-0.5x^2-2x+440=0

a = -0.5; b = -2; c = +440;
Δ = b2-4ac
Δ = -22-4·(-0.5)·440
Δ = 884
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:

$\sqrt{\Delta}=\sqrt{884}=\sqrt{4*221}=\sqrt{4}*\sqrt{221}=2\sqrt{221}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{221}}{2*-0.5}=\frac{2-2\sqrt{221}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{221}}{2*-0.5}=\frac{2+2\sqrt{221}}{-1}
$