3-6x^2+2x^2=-85

Solution for 3-6x^2+2x^2=-85 equation:

3-6x^2+2x^2=-85

We move all terms to the left:

3-6x^2+2x^2-(-85)=0

We add all the numbers together, and all the variables

-4x^2+88=0

a = -4; b = 0; c = +88;
Δ = b2-4ac
Δ = 02-4·(-4)·88
Δ = 1408
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:

$\sqrt{\Delta}=\sqrt{1408}=\sqrt{64*22}=\sqrt{64}*\sqrt{22}=8\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{22}}{2*-4}=\frac{0-8\sqrt{22}}{-8}
=-\frac{8\sqrt{22}}{-8}
=-\frac{\sqrt{22}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{22}}{2*-4}=\frac{0+8\sqrt{22}}{-8}
=\frac{8\sqrt{22}}{-8}
=\frac{\sqrt{22}}{-1}
$