0.25x^2+x+1=0.5

Solution for 0.25x^2+x+1=0.5 equation:

0.25x^2+x+1=0.5

We move all terms to the left:

0.25x^2+x+1-(0.5)=0

We add all the numbers together, and all the variables

0.25x^2+x+0.5=0

a = 0.25; b = 1; c = +0.5;
Δ = b2-4ac
Δ = 12-4·0.25·0.5
Δ = 0.5
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{-(1)-\sqrt{0.5}}{2*0.25}=\frac{-1-\sqrt{0.5}}{0.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{0.5}}{2*0.25}=\frac{-1+\sqrt{0.5}}{0.5}
$