0.5x^2-6x=-9

Solution for 0.5x^2-6x=-9 equation:

0.5x^2-6x=-9

We move all terms to the left:

0.5x^2-6x-(-9)=0

We add all the numbers together, and all the variables

0.5x^2-6x+9=0

a = 0.5; b = -6; c = +9;
Δ = b2-4ac
Δ = -62-4·0.5·9
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{-(-6)-3\sqrt{2}}{2*0.5}=\frac{6-3\sqrt{2}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+3\sqrt{2}}{2*0.5}=\frac{6+3\sqrt{2}}{1}
$