.15x^2-46x+1200=0

Solution for .15x^2-46x+1200=0 equation:

.15x^2-46x+1200=0

a = .15; b = -46; c = +1200;
Δ = b2-4ac
Δ = -462-4·.15·1200
Δ = 1396
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:

$\sqrt{\Delta}=\sqrt{1396}=\sqrt{4*349}=\sqrt{4}*\sqrt{349}=2\sqrt{349}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{349}}{2*.15}=\frac{46-2\sqrt{349}}{0.3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{349}}{2*.15}=\frac{46+2\sqrt{349}}{0.3}
$