542=0.5x^2+10x+200

Solution for 542=0.5x^2+10x+200 equation:

542=0.5x^2+10x+200

We move all terms to the left:

542-(0.5x^2+10x+200)=0

We get rid of parentheses

-0.5x^2-10x-200+542=0

We add all the numbers together, and all the variables

-0.5x^2-10x+342=0

a = -0.5; b = -10; c = +342;
Δ = b2-4ac
Δ = -102-4·(-0.5)·342
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-28}{2*-0.5}=\frac{-18}{-1}
=+18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+28}{2*-0.5}=\frac{38}{-1}
=-38
$