8+3x=1/4x-16

Solution for 8+3x=1/4x-16 equation:

8+3x=1/4x-16

We move all terms to the left:

8+3x-(1/4x-16)=0


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

x∈R


We get rid of parentheses

3x-1/4x+16+8=0

We multiply all the terms by the denominator


3x*4x+16*4x+8*4x-1=0

Wy multiply elements

12x^2+64x+32x-1=0

We add all the numbers together, and all the variables

12x^2+96x-1=0

a = 12; b = 96; c = -1;
Δ = b2-4ac
Δ = 962-4·12·(-1)
Δ = 9264
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:

$\sqrt{\Delta}=\sqrt{9264}=\sqrt{16*579}=\sqrt{16}*\sqrt{579}=4\sqrt{579}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-4\sqrt{579}}{2*12}=\frac{-96-4\sqrt{579}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+4\sqrt{579}}{2*12}=\frac{-96+4\sqrt{579}}{24}
$