11/3*x^2-7=0

Solution for 11/3*x^2-7=0 equation:

11/3x^2-7=0


Domain of the equation: 3x^2!=0

x^2!=0/3

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-7*3x^2+11=0

Wy multiply elements

-21x^2+11=0

a = -21; b = 0; c = +11;
Δ = b2-4ac
Δ = 02-4·(-21)·11
Δ = 924
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:

$\sqrt{\Delta}=\sqrt{924}=\sqrt{4*231}=\sqrt{4}*\sqrt{231}=2\sqrt{231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{231}}{2*-21}=\frac{0-2\sqrt{231}}{-42}
=-\frac{2\sqrt{231}}{-42}
=-\frac{\sqrt{231}}{-21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{231}}{2*-21}=\frac{0+2\sqrt{231}}{-42}
=\frac{2\sqrt{231}}{-42}
=\frac{\sqrt{231}}{-21}
$