.6x^2-30x+187.5=0

Solution for .6x^2-30x+187.5=0 equation:

.6x^2-30x+187.5=0

a = .6; b = -30; c = +187.5;
Δ = b2-4ac
Δ = -302-4·.6·187.5
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*.6}=\frac{30-15\sqrt{2}}{1.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+15\sqrt{2}}{2*.6}=\frac{30+15\sqrt{2}}{1.2}
$