0.25x^2-0.25x-10.5=0

Solution for 0.25x^2-0.25x-10.5=0 equation:

0.25x^2-0.25x-10.5=0

a = 0.25; b = -0.25; c = -10.5;
Δ = b2-4ac
Δ = -0.252-4·0.25·(-10.5)
Δ = 10.5625
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{-(-0.25)-\sqrt{10.5625}}{2*0.25}=\frac{0.25-\sqrt{10.5625}}{0.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.25)+\sqrt{10.5625}}{2*0.25}=\frac{0.25+\sqrt{10.5625}}{0.5}
$