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

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

X-3=2X^2-4X-6

We move all terms to the left:

X-3-(2X^2-4X-6)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2X^2+5X+3=0

a = -2; b = 5; c = +3;
Δ = b2-4ac
Δ = 52-4·(-2)·3
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-7}{2*-2}=\frac{-12}{-4}
=+3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+7}{2*-2}=\frac{2}{-4}
=-1/2
$