-1.5x^2+75=0

Solution for -1.5x^2+75=0 equation:

-1.5x^2+75=0

a = -1.5; b = 0; c = +75;
Δ = b2-4ac
Δ = 02-4·(-1.5)·75
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{-(0)-15\sqrt{2}}{2*-1.5}=\frac{0-15\sqrt{2}}{-3}
=-\frac{15\sqrt{2}}{-3}
=-\frac{5\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+15\sqrt{2}}{2*-1.5}=\frac{0+15\sqrt{2}}{-3}
=\frac{15\sqrt{2}}{-3}
=\frac{5\sqrt{2}}{-1}
$