2(4x2)=4x-12(x-1)

Solution for 2(4x2)=4x-12(x-1) equation:

2(4x^2)=4x-12(x-1)

We move all terms to the left:

2(4x^2)-(4x-12(x-1))=0


We calculate terms in parentheses: -(4x-12(x-1)), so:

4x-12(x-1)

We multiply parentheses

4x-12x+12

We add all the numbers together, and all the variables

-8x+12

Back to the equation:

-(-8x+12)


We get rid of parentheses

24x^2+8x-12=0

a = 24; b = 8; c = -12;
Δ = b2-4ac
Δ = 82-4·24·(-12)
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{19}}{2*24}=\frac{-8-8\sqrt{19}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{19}}{2*24}=\frac{-8+8\sqrt{19}}{48}
$