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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

3x^2*2+x*2-5=0

Wy multiply elements

6x^2+2x-5=0

a = 6; b = 2; c = -5;
Δ = b2-4ac
Δ = 22-4·6·(-5)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{31}}{2*6}=\frac{-2-2\sqrt{31}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{31}}{2*6}=\frac{-2+2\sqrt{31}}{12}
$