-12x^2+38=0

Solution for -12x^2+38=0 equation:

-12x^2+38=0

a = -12; b = 0; c = +38;
Δ = b2-4ac
Δ = 02-4·(-12)·38
Δ = 1824
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:

$\sqrt{\Delta}=\sqrt{1824}=\sqrt{16*114}=\sqrt{16}*\sqrt{114}=4\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{114}}{2*-12}=\frac{0-4\sqrt{114}}{-24}
=-\frac{4\sqrt{114}}{-24}
=-\frac{\sqrt{114}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{114}}{2*-12}=\frac{0+4\sqrt{114}}{-24}
=\frac{4\sqrt{114}}{-24}
=\frac{\sqrt{114}}{-6}
$