3/4x^2+1=30

Solution for 3/4x^2+1=30 equation:

3/4x^2+1=30

We move all terms to the left:

3/4x^2+1-(30)=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

3/4x^2-29=0

We multiply all the terms by the denominator


-29*4x^2+3=0

Wy multiply elements

-116x^2+3=0

a = -116; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-116)·3
Δ = 1392
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:

$\sqrt{\Delta}=\sqrt{1392}=\sqrt{16*87}=\sqrt{16}*\sqrt{87}=4\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{87}}{2*-116}=\frac{0-4\sqrt{87}}{-232}
=-\frac{4\sqrt{87}}{-232}
=-\frac{\sqrt{87}}{-58}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{87}}{2*-116}=\frac{0+4\sqrt{87}}{-232}
=\frac{4\sqrt{87}}{-232}
=\frac{\sqrt{87}}{-58}
$