8-0.25x=0.5x2

Solution for 8-0.25x=0.5x2 equation:

8-0.25x=0.5x^2

We move all terms to the left:

8-0.25x-(0.5x^2)=0

We get rid of parentheses

-0.5x^2-0.25x+8=0

a = -0.5; b = -0.25; c = +8;
Δ = b2-4ac
Δ = -0.252-4·(-0.5)·8
Δ = 16.0625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.25)-\sqrt{16.0625}}{2*-0.5}=\frac{0.25-\sqrt{16.0625}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.25)+\sqrt{16.0625}}{2*-0.5}=\frac{0.25+\sqrt{16.0625}}{-1}
$