3/4x^2+1=31

Solution for 3/4x^2+1=31 equation:

3/4x^2+1=31

We move all terms to the left:

3/4x^2+1-(31)=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^2-30=0

We multiply all the terms by the denominator


-30*4x^2+3=0

Wy multiply elements

-120x^2+3=0

a = -120; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-120)·3
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{10}}{2*-120}=\frac{0-12\sqrt{10}}{-240}
=-\frac{12\sqrt{10}}{-240}
=-\frac{\sqrt{10}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{10}}{2*-120}=\frac{0+12\sqrt{10}}{-240}
=\frac{12\sqrt{10}}{-240}
=\frac{\sqrt{10}}{-20}
$