4(x-3)=8(x-2)4x

Solution for 4(x-3)=8(x-2)4x equation:

4(x-3)=8(x-2)4x

We move all terms to the left:

4(x-3)-(8(x-2)4x)=0

We multiply parentheses

4x-(8(x-2)4x)-12=0


We calculate terms in parentheses: -(8(x-2)4x), so:

8(x-2)4x

We multiply parentheses

32x^2-64x

Back to the equation:

-(32x^2-64x)


We get rid of parentheses

-32x^2+4x+64x-12=0

We add all the numbers together, and all the variables

-32x^2+68x-12=0

a = -32; b = 68; c = -12;
Δ = b2-4ac
Δ = 682-4·(-32)·(-12)
Δ = 3088
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:

$\sqrt{\Delta}=\sqrt{3088}=\sqrt{16*193}=\sqrt{16}*\sqrt{193}=4\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-4\sqrt{193}}{2*-32}=\frac{-68-4\sqrt{193}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+4\sqrt{193}}{2*-32}=\frac{-68+4\sqrt{193}}{-64}
$