-2x^2+6x+1=-3x^2

Solution for -2x^2+6x+1=-3x^2 equation:

-2x^2+6x+1=-3x^2

We move all terms to the left:

-2x^2+6x+1-(-3x^2)=0

We get rid of parentheses

-2x^2+3x^2+6x+1=0

We add all the numbers together, and all the variables

x^2+6x+1=0

a = 1; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·1·1
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{2}}{2*1}=\frac{-6-4\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{2}}{2*1}=\frac{-6+4\sqrt{2}}{2}
$