1/8x+5=21X=

Solution for 1/8x+5=21X= equation:

1/8x+5=21x=

We move all terms to the left:

1/8x+5-(21x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-21x+1/8x+5=0

We multiply all the terms by the denominator


-21x*8x+5*8x+1=0

Wy multiply elements

-168x^2+40x+1=0

a = -168; b = 40; c = +1;
Δ = b2-4ac
Δ = 402-4·(-168)·1
Δ = 2272
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:

$\sqrt{\Delta}=\sqrt{2272}=\sqrt{16*142}=\sqrt{16}*\sqrt{142}=4\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{142}}{2*-168}=\frac{-40-4\sqrt{142}}{-336}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{142}}{2*-168}=\frac{-40+4\sqrt{142}}{-336}
$