8x+4=1/4x-16

Solution for 8x+4=1/4x-16 equation:

8x+4=1/4x-16

We move all terms to the left:

8x+4-(1/4x-16)=0


Domain of the equation: 4x-16)!=0

x∈R


We get rid of parentheses

8x-1/4x+16+4=0

We multiply all the terms by the denominator


8x*4x+16*4x+4*4x-1=0

Wy multiply elements

32x^2+64x+16x-1=0

We add all the numbers together, and all the variables

32x^2+80x-1=0

a = 32; b = 80; c = -1;
Δ = b2-4ac
Δ = 802-4·32·(-1)
Δ = 6528
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:

$\sqrt{\Delta}=\sqrt{6528}=\sqrt{64*102}=\sqrt{64}*\sqrt{102}=8\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-8\sqrt{102}}{2*32}=\frac{-80-8\sqrt{102}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+8\sqrt{102}}{2*32}=\frac{-80+8\sqrt{102}}{64}
$