2/3*x^2=26

Solution for 2/3*x^2=26 equation:

2/3x^2=26

We move all terms to the left:

2/3x^2-(26)=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


-26*3x^2+2=0

Wy multiply elements

-78x^2+2=0

a = -78; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-78)·2
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{39}}{2*-78}=\frac{0-4\sqrt{39}}{-156}
=-\frac{4\sqrt{39}}{-156}
=-\frac{\sqrt{39}}{-39}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{39}}{2*-78}=\frac{0+4\sqrt{39}}{-156}
=\frac{4\sqrt{39}}{-156}
=\frac{\sqrt{39}}{-39}
$