4-6x2=-(3x-1)

Solution for 4-6x2=-(3x-1) equation:

4-6x^2=-(3x-1)

We move all terms to the left:

4-6x^2-(-(3x-1))=0


We calculate terms in parentheses: -(-(3x-1)), so:

-(3x-1)

We get rid of parentheses

-3x+1

Back to the equation:

-(-3x+1)


We get rid of parentheses

-6x^2+3x-1+4=0

We add all the numbers together, and all the variables

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

a = -6; b = 3; c = +3;
Δ = b2-4ac
Δ = 32-4·(-6)·3
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9}{2*-6}=\frac{-12}{-12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9}{2*-6}=\frac{6}{-12}
=-1/2
$