0.5x^2=12-2x

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

0.5x^2=12-2x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

0.5x^2+2x-12=0

a = 0.5; b = 2; c = -12;
Δ = b2-4ac
Δ = 22-4·0.5·(-12)
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{7}}{2*0.5}=\frac{-2-2\sqrt{7}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{7}}{2*0.5}=\frac{-2+2\sqrt{7}}{1}
$