2/3x^2=62

Solution for 2/3x^2=62 equation:

2/3x^2=62

We move all terms to the left:

2/3x^2-(62)=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


-62*3x^2+2=0

Wy multiply elements

-186x^2+2=0

a = -186; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-186)·2
Δ = 1488
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:

$\sqrt{\Delta}=\sqrt{1488}=\sqrt{16*93}=\sqrt{16}*\sqrt{93}=4\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{93}}{2*-186}=\frac{0-4\sqrt{93}}{-372}
=-\frac{4\sqrt{93}}{-372}
=-\frac{\sqrt{93}}{-93}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{93}}{2*-186}=\frac{0+4\sqrt{93}}{-372}
=\frac{4\sqrt{93}}{-372}
=\frac{\sqrt{93}}{-93}
$