3/4x2-4=16

Solution for 3/4x2-4=16 equation:

3/4x^2-4=16

We move all terms to the left:

3/4x^2-4-(16)=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^2-20=0

We multiply all the terms by the denominator


-20*4x^2+3=0

Wy multiply elements

-80x^2+3=0

a = -80; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-80)·3
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*-80}=\frac{0-8\sqrt{15}}{-160}
=-\frac{8\sqrt{15}}{-160}
=-\frac{\sqrt{15}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{15}}{2*-80}=\frac{0+8\sqrt{15}}{-160}
=\frac{8\sqrt{15}}{-160}
=\frac{\sqrt{15}}{-20}
$