0.5x^2-2x-6=10

Solution for 0.5x^2-2x-6=10 equation:

0.5x^2-2x-6=10

We move all terms to the left:

0.5x^2-2x-6-(10)=0

We add all the numbers together, and all the variables

0.5x^2-2x-16=0

a = 0.5; b = -2; c = -16;
Δ = b2-4ac
Δ = -22-4·0.5·(-16)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6}{2*0.5}=\frac{-4}{1}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6}{2*0.5}=\frac{8}{1}
=8
$