1/3x2-7=43

Solution for 1/3x2-7=43 equation:

1/3x^2-7=43

We move all terms to the left:

1/3x^2-7-(43)=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^2-50=0

We multiply all the terms by the denominator


-50*3x^2+1=0

Wy multiply elements

-150x^2+1=0

a = -150; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-150)·1
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{6}}{2*-150}=\frac{0-10\sqrt{6}}{-300}
=-\frac{10\sqrt{6}}{-300}
=-\frac{\sqrt{6}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{6}}{2*-150}=\frac{0+10\sqrt{6}}{-300}
=\frac{10\sqrt{6}}{-300}
=\frac{\sqrt{6}}{-30}
$