1/10x^2+2=82

Solution for 1/10x^2+2=82 equation:

1/10x^2+2=82

We move all terms to the left:

1/10x^2+2-(82)=0


Domain of the equation: 10x^2!=0

x^2!=0/10

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

1/10x^2-80=0

We multiply all the terms by the denominator


-80*10x^2+1=0

Wy multiply elements

-800x^2+1=0

a = -800; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-800)·1
Δ = 3200
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:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{2}}{2*-800}=\frac{0-40\sqrt{2}}{-1600}
=-\frac{40\sqrt{2}}{-1600}
=-\frac{\sqrt{2}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{2}}{2*-800}=\frac{0+40\sqrt{2}}{-1600}
=\frac{40\sqrt{2}}{-1600}
=\frac{\sqrt{2}}{-40}
$