-1/4x^2+30=0

Solution for -1/4x^2+30=0 equation:

-1/4x^2+30=0


Domain of the equation: 4x^2!=0

x^2!=0/4

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


30*4x^2-1=0

Wy multiply elements

120x^2-1=0

a = 120; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·120·(-1)
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*120}=\frac{0-4\sqrt{30}}{240}
=-\frac{4\sqrt{30}}{240}
=-\frac{\sqrt{30}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*120}=\frac{0+4\sqrt{30}}{240}
=\frac{4\sqrt{30}}{240}
=\frac{\sqrt{30}}{60}
$