2(x-3)2x=10-4(x-1)

Solution for 2(x-3)2x=10-4(x-1) equation:

2(x-3)2x=10-4(x-1)

We move all terms to the left:

2(x-3)2x-(10-4(x-1))=0

We multiply parentheses

4x^2-12x-(10-4(x-1))=0


We calculate terms in parentheses: -(10-4(x-1)), so:

10-4(x-1)

determiningTheFunctionDomain
-4(x-1)+10

We multiply parentheses

-4x+4+10

We add all the numbers together, and all the variables

-4x+14

Back to the equation:

-(-4x+14)


We get rid of parentheses

4x^2-12x+4x-14=0

We add all the numbers together, and all the variables

4x^2-8x-14=0

a = 4; b = -8; c = -14;
Δ = b2-4ac
Δ = -82-4·4·(-14)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12\sqrt{2}}{2*4}=\frac{8-12\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12\sqrt{2}}{2*4}=\frac{8+12\sqrt{2}}{8}
$