3.5=-0.5x^2+8

Solution for 3.5=-0.5x^2+8 equation:

3.5=-0.5x^2+8

We move all terms to the left:

3.5-(-0.5x^2+8)=0

We get rid of parentheses

0.5x^2-8+3.5=0

We add all the numbers together, and all the variables

0.5x^2-4.5=0

a = 0.5; b = 0; c = -4.5;
Δ = b2-4ac
Δ = 02-4·0.5·(-4.5)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3}{2*0.5}=\frac{-3}{1}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3}{2*0.5}=\frac{3}{1}
=3
$