X2-0.5x-3=0

Solution for X2-0.5x-3=0 equation:

X2-0.5X-3=0

We add all the numbers together, and all the variables

X^2-0.5X-3=0

a = 1; b = -0.5; c = -3;
Δ = b2-4ac
Δ = -0.52-4·1·(-3)
Δ = 12.25
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{-(-0.5)-\sqrt{12.25}}{2*1}=\frac{0.5-\sqrt{12.25}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5)+\sqrt{12.25}}{2*1}=\frac{0.5+\sqrt{12.25}}{2}
$