12x^2-5/2=0

Solution for 12x^2-5/2=0 equation:

12x^2-5/2=0

We multiply all the terms by the denominator


12x^2*2-5=0

Wy multiply elements

24x^2-5=0

a = 24; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·24·(-5)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*24}=\frac{0-4\sqrt{30}}{48}
=-\frac{4\sqrt{30}}{48}
=-\frac{\sqrt{30}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*24}=\frac{0+4\sqrt{30}}{48}
=\frac{4\sqrt{30}}{48}
=\frac{\sqrt{30}}{12}
$