x^2+4x-2=2x^2-3x+6

Solution for x^2+4x-2=2x^2-3x+6 equation:

x^2+4x-2=2x^2-3x+6

We move all terms to the left:

x^2+4x-2-(2x^2-3x+6)=0

We get rid of parentheses

x^2-2x^2+4x+3x-6-2=0

We add all the numbers together, and all the variables

-1x^2+7x-8=0

a = -1; b = 7; c = -8;
Δ = b2-4ac
Δ = 72-4·(-1)·(-8)
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{17}}{2*-1}=\frac{-7-\sqrt{17}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{17}}{2*-1}=\frac{-7+\sqrt{17}}{-2}
$