2x^2-x+0.25=8.25

Solution for 2x^2-x+0.25=8.25 equation:

2x^2-x+0.25=8.25

We move all terms to the left:

2x^2-x+0.25-(8.25)=0

We add all the numbers together, and all the variables

2x^2-1x-8=0

a = 2; b = -1; c = -8;
Δ = b2-4ac
Δ = -12-4·2·(-8)
Δ = 65
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{65}}{2*2}=\frac{1-\sqrt{65}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{65}}{2*2}=\frac{1+\sqrt{65}}{4}
$