1/4x^2+8=38

Solution for 1/4x^2+8=38 equation:

1/4x^2+8=38

We move all terms to the left:

1/4x^2+8-(38)=0


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

x^2!=0/4

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x^2-30=0

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}
$