3/4x^2+2=16

Solution for 3/4x^2+2=16 equation:

3/4x^2+2=16

We move all terms to the left:

3/4x^2+2-(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^2-14=0

We multiply all the terms by the denominator


-14*4x^2+3=0

Wy multiply elements

-56x^2+3=0

a = -56; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-56)·3
Δ = 672
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:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{42}}{2*-56}=\frac{0-4\sqrt{42}}{-112}
=-\frac{4\sqrt{42}}{-112}
=-\frac{\sqrt{42}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{42}}{2*-56}=\frac{0+4\sqrt{42}}{-112}
=\frac{4\sqrt{42}}{-112}
=\frac{\sqrt{42}}{-28}
$