1/2x-4=-8x+12

Solution for 1/2x-4=-8x+12 equation:

1/2x-4=-8x+12

We move all terms to the left:

1/2x-4-(-8x+12)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x+8x-12-4=0

We multiply all the terms by the denominator


8x*2x-12*2x-4*2x+1=0

Wy multiply elements

16x^2-24x-8x+1=0

We add all the numbers together, and all the variables

16x^2-32x+1=0

a = 16; b = -32; c = +1;
Δ = b2-4ac
Δ = -322-4·16·1
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{15}}{2*16}=\frac{32-8\sqrt{15}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{15}}{2*16}=\frac{32+8\sqrt{15}}{32}
$