4.5x^2-18x-45=0

Solution for 4.5x^2-18x-45=0 equation:

4.5x^2-18x-45=0

a = 4.5; b = -18; c = -45;
Δ = b2-4ac
Δ = -182-4·4.5·(-45)
Δ = 1134
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:

$\sqrt{\Delta}=\sqrt{1134}=\sqrt{81*14}=\sqrt{81}*\sqrt{14}=9\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-9\sqrt{14}}{2*4.5}=\frac{18-9\sqrt{14}}{9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+9\sqrt{14}}{2*4.5}=\frac{18+9\sqrt{14}}{9}
$