0.5x^2+3x=33

Solution for 0.5x^2+3x=33 equation:

0.5x^2+3x=33

We move all terms to the left:

0.5x^2+3x-(33)=0

a = 0.5; b = 3; c = -33;
Δ = b2-4ac
Δ = 32-4·0.5·(-33)
Δ = 75
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:

$\sqrt{\Delta}=\sqrt{75}=\sqrt{25*3}=\sqrt{25}*\sqrt{3}=5\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-5\sqrt{3}}{2*0.5}=\frac{-3-5\sqrt{3}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+5\sqrt{3}}{2*0.5}=\frac{-3+5\sqrt{3}}{1}
$