9-82x2=6

Solution for 9-82x2=6 equation:

9-82x^2=6

We move all terms to the left:

9-82x^2-(6)=0

We add all the numbers together, and all the variables

-82x^2+3=0

a = -82; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-82)·3
Δ = 984
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:

$\sqrt{\Delta}=\sqrt{984}=\sqrt{4*246}=\sqrt{4}*\sqrt{246}=2\sqrt{246}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{246}}{2*-82}=\frac{0-2\sqrt{246}}{-164}
=-\frac{2\sqrt{246}}{-164}
=-\frac{\sqrt{246}}{-82}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{246}}{2*-82}=\frac{0+2\sqrt{246}}{-164}
=\frac{2\sqrt{246}}{-164}
=\frac{\sqrt{246}}{-82}
$