32=0.5x^2+6x+11

Solution for 32=0.5x^2+6x+11 equation:

32=0.5x^2+6x+11

We move all terms to the left:

32-(0.5x^2+6x+11)=0

We get rid of parentheses

-0.5x^2-6x-11+32=0

We add all the numbers together, and all the variables

-0.5x^2-6x+21=0

a = -0.5; b = -6; c = +21;
Δ = b2-4ac
Δ = -62-4·(-0.5)·21
Δ = 78
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-\sqrt{78}}{2*-0.5}=\frac{6-\sqrt{78}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+\sqrt{78}}{2*-0.5}=\frac{6+\sqrt{78}}{-1}
$