2/5x^2=12

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

2/5x^2=12

We move all terms to the left:

2/5x^2-(12)=0


Domain of the equation: 5x^2!=0

x^2!=0/5

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-12*5x^2+2=0

Wy multiply elements

-60x^2+2=0

a = -60; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-60)·2
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*-60}=\frac{0-4\sqrt{30}}{-120}
=-\frac{4\sqrt{30}}{-120}
=-\frac{\sqrt{30}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*-60}=\frac{0+4\sqrt{30}}{-120}
=\frac{4\sqrt{30}}{-120}
=\frac{\sqrt{30}}{-30}
$