4/5x2-12=0

Solution for 4/5x2-12=0 equation:

4/5x^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+4=0

Wy multiply elements

-60x^2+4=0

a = -60; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-60)·4
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{15}}{2*-60}=\frac{0-8\sqrt{15}}{-120}
=-\frac{8\sqrt{15}}{-120}
=-\frac{\sqrt{15}}{-15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{15}}{2*-60}=\frac{0+8\sqrt{15}}{-120}
=\frac{8\sqrt{15}}{-120}
=\frac{\sqrt{15}}{-15}
$