1/8x+21+3x=12x-4

Solution for 1/8x+21+3x=12x-4 equation:

1/8x+21+3x=12x-4

We move all terms to the left:

1/8x+21+3x-(12x-4)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/8x-(12x-4)+21=0

We get rid of parentheses

3x+1/8x-12x+4+21=0

We multiply all the terms by the denominator


3x*8x-12x*8x+4*8x+21*8x+1=0

Wy multiply elements

24x^2-96x^2+32x+168x+1=0

We add all the numbers together, and all the variables

-72x^2+200x+1=0

a = -72; b = 200; c = +1;
Δ = b2-4ac
Δ = 2002-4·(-72)·1
Δ = 40288
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:

$\sqrt{\Delta}=\sqrt{40288}=\sqrt{16*2518}=\sqrt{16}*\sqrt{2518}=4\sqrt{2518}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-4\sqrt{2518}}{2*-72}=\frac{-200-4\sqrt{2518}}{-144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+4\sqrt{2518}}{2*-72}=\frac{-200+4\sqrt{2518}}{-144}
$