3x^2+6=5x^2-194

Solution for 3x^2+6=5x^2-194 equation:

3x^2+6=5x^2-194

We move all terms to the left:

3x^2+6-(5x^2-194)=0

We get rid of parentheses

3x^2-5x^2+194+6=0

We add all the numbers together, and all the variables

-2x^2+200=0

a = -2; b = 0; c = +200;
Δ = b2-4ac
Δ = 02-4·(-2)·200
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40}{2*-2}=\frac{-40}{-4}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40}{2*-2}=\frac{40}{-4}
=-10
$