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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-6x-7=0

a = 1; b = -6; c = -7;
Δ = b2-4ac
Δ = -62-4·1·(-7)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-8}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+8}{2*1}=\frac{14}{2}
=7
$