0.25x^2-6x+12=0

Solution for 0.25x^2-6x+12=0 equation:

0.25x^2-6x+12=0

a = 0.25; b = -6; c = +12;
Δ = b2-4ac
Δ = -62-4·0.25·12
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{6}}{2*0.25}=\frac{6-2\sqrt{6}}{0.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{6}}{2*0.25}=\frac{6+2\sqrt{6}}{0.5}
$