0.5x^2-30x+225=0

Solution for 0.5x^2-30x+225=0 equation:

0.5x^2-30x+225=0

a = 0.5; b = -30; c = +225;
Δ = b2-4ac
Δ = -302-4·0.5·225
Δ = 450
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:

$\sqrt{\Delta}=\sqrt{450}=\sqrt{225*2}=\sqrt{225}*\sqrt{2}=15\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-15\sqrt{2}}{2*0.5}=\frac{30-15\sqrt{2}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+15\sqrt{2}}{2*0.5}=\frac{30+15\sqrt{2}}{1}
$