13.5-9x-0.5x^2=0

Solution for 13.5-9x-0.5x^2=0 equation:

13.5-9x-0.5x^2=0

a = -0.5; b = -9; c = +13.5;
Δ = b2-4ac
Δ = -92-4·(-0.5)·13.5
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-6\sqrt{3}}{2*-0.5}=\frac{9-6\sqrt{3}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+6\sqrt{3}}{2*-0.5}=\frac{9+6\sqrt{3}}{-1}
$