2/4x+8=x-16

Solution for 2/4x+8=x-16 equation:

2/4x+8=x-16

We move all terms to the left:

2/4x+8-(x-16)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

2/4x-x+16+8=0

We multiply all the terms by the denominator


-x*4x+16*4x+8*4x+2=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-4x^2+96x+2=0

a = -4; b = 96; c = +2;
Δ = b2-4ac
Δ = 962-4·(-4)·2
Δ = 9248
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:

$\sqrt{\Delta}=\sqrt{9248}=\sqrt{4624*2}=\sqrt{4624}*\sqrt{2}=68\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-68\sqrt{2}}{2*-4}=\frac{-96-68\sqrt{2}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+68\sqrt{2}}{2*-4}=\frac{-96+68\sqrt{2}}{-8}
$