0.25q^2-q-5=0

Solution for 0.25q^2-q-5=0 equation:

0.25q^2-q-5=0

We add all the numbers together, and all the variables

0.25q^2-1q-5=0

a = 0.25; b = -1; c = -5;
Δ = b2-4ac
Δ = -12-4·0.25·(-5)
Δ = 6
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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