6-1/3x^2=-19

Solution for 6-1/3x^2=-19 equation:

6-1/3x^2=-19

We move all terms to the left:

6-1/3x^2-(-19)=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+25=0

We multiply all the terms by the denominator


25*3x^2-1=0

Wy multiply elements

75x^2-1=0

a = 75; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·75·(-1)
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{3}}{2*75}=\frac{0-10\sqrt{3}}{150}
=-\frac{10\sqrt{3}}{150}
=-\frac{\sqrt{3}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{3}}{2*75}=\frac{0+10\sqrt{3}}{150}
=\frac{10\sqrt{3}}{150}
=\frac{\sqrt{3}}{15}
$