(1/2)(x)=2x^2-3x-6

Solution for (1/2)(x)=2x^2-3x-6 equation:

(1/2)(x)=2x^2-3x-6

We move all terms to the left:

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


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -1; b = 3; c = +6;
Δ = b2-4ac
Δ = 32-4·(-1)·6
Δ = 33
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{-(3)-\sqrt{33}}{2*-1}=\frac{-3-\sqrt{33}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{33}}{2*-1}=\frac{-3+\sqrt{33}}{-2}
$