0.5x^2-x=12

Solution for 0.5x^2-x=12 equation:

0.5x^2-x=12

We move all terms to the left:

0.5x^2-x-(12)=0

We add all the numbers together, and all the variables

0.5x^2-1x-12=0

a = 0.5; b = -1; c = -12;
Δ = b2-4ac
Δ = -12-4·0.5·(-12)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5}{2*0.5}=\frac{-4}{1}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*0.5}=\frac{6}{1}
=6
$