6-1/3x^2=-70

Solution for 6-1/3x^2=-70 equation:

6-1/3x^2=-70

We move all terms to the left:

6-1/3x^2-(-70)=0


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

x^2!=0/3

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

-1/3x^2+76=0

We multiply all the terms by the denominator


76*3x^2-1=0

Wy multiply elements

228x^2-1=0

a = 228; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·228·(-1)
Δ = 912
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:

$\sqrt{\Delta}=\sqrt{912}=\sqrt{16*57}=\sqrt{16}*\sqrt{57}=4\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{57}}{2*228}=\frac{0-4\sqrt{57}}{456}
=-\frac{4\sqrt{57}}{456}
=-\frac{\sqrt{57}}{114}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{57}}{2*228}=\frac{0+4\sqrt{57}}{456}
=\frac{4\sqrt{57}}{456}
=\frac{\sqrt{57}}{114}
$