2x-1/8x=30

Solution for 2x-1/8x=30 equation:

2x-1/8x=30

We move all terms to the left:

2x-1/8x-(30)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We multiply all the terms by the denominator


2x*8x-30*8x-1=0

Wy multiply elements

16x^2-240x-1=0

a = 16; b = -240; c = -1;
Δ = b2-4ac
Δ = -2402-4·16·(-1)
Δ = 57664
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:

$\sqrt{\Delta}=\sqrt{57664}=\sqrt{64*901}=\sqrt{64}*\sqrt{901}=8\sqrt{901}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-8\sqrt{901}}{2*16}=\frac{240-8\sqrt{901}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+8\sqrt{901}}{2*16}=\frac{240+8\sqrt{901}}{32}
$