0.5x^2+3=12

Solution for 0.5x^2+3=12 equation:

0.5x^2+3=12

We move all terms to the left:

0.5x^2+3-(12)=0

We add all the numbers together, and all the variables

0.5x^2-9=0

a = 0.5; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·0.5·(-9)
Δ = 18
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:

$\sqrt{\Delta}=\sqrt{18}=\sqrt{9*2}=\sqrt{9}*\sqrt{2}=3\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{2}}{2*0.5}=\frac{0-3\sqrt{2}}{1}
=-\frac{3\sqrt{2}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{2}}{2*0.5}=\frac{0+3\sqrt{2}}{1}
=\frac{3\sqrt{2}}{1}
$