x^2-(10^0.25)*x-(10^0.25)*0.25=0

Solution for x^2-(10^0.25)*x-(10^0.25)*0.25=0 equation:

x^2-(10^0.25)*x-(10^0.25)*0.25=0

We add all the numbers together, and all the variables

x^2-(10^0.25)*x-0.44456985251=0

We multiply parentheses

x^2-10x-0.44456985251=0

a = 1; b = -10; c = -0.44456985251;
Δ = b2-4ac
Δ = -102-4·1·(-0.44456985251)
Δ = 101.77827941
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{-(-10)-\sqrt{101.77827941}}{2*1}=\frac{10-\sqrt{101.77827941}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+\sqrt{101.77827941}}{2*1}=\frac{10+\sqrt{101.77827941}}{2}
$