x^2+4/3-9=0

Solution for x^2+4/3-9=0 equation:

x^2+4/3-9=0

We multiply all the terms by the denominator


x^2*3+4-9*3=0

We add all the numbers together, and all the variables

x^2*3-23=0

Wy multiply elements

3x^2-23=0

a = 3; b = 0; c = -23;
Δ = b2-4ac
Δ = 02-4·3·(-23)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{69}}{2*3}=\frac{0-2\sqrt{69}}{6}
=-\frac{2\sqrt{69}}{6}
=-\frac{\sqrt{69}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{69}}{2*3}=\frac{0+2\sqrt{69}}{6}
=\frac{2\sqrt{69}}{6}
=\frac{\sqrt{69}}{3}
$