4(x-1)=2(6-x2)

Solution for 4(x-1)=2(6-x2) equation:

4(x-1)=2(6-x2)

We move all terms to the left:

4(x-1)-(2(6-x2))=0

We add all the numbers together, and all the variables

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

We multiply parentheses

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


We calculate terms in parentheses: -(2(-1x^2+6)), so:

2(-1x^2+6)

We multiply parentheses

-2x^2+12

Back to the equation:

-(-2x^2+12)


We get rid of parentheses

2x^2+4x-12-4=0

We add all the numbers together, and all the variables

2x^2+4x-16=0

a = 2; b = 4; c = -16;
Δ = b2-4ac
Δ = 42-4·2·(-16)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-12}{2*2}=\frac{-16}{4}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+12}{2*2}=\frac{8}{4}
=2
$