2x=157/8x

Solution for 2x=157/8x equation:

2x=157/8x

We move all terms to the left:

2x-(157/8x)=0


Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+157/8x)=0

We get rid of parentheses

2x-157/8x=0

We multiply all the terms by the denominator


2x*8x-157=0

Wy multiply elements

16x^2-157=0

a = 16; b = 0; c = -157;
Δ = b2-4ac
Δ = 02-4·16·(-157)
Δ = 10048
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:

$\sqrt{\Delta}=\sqrt{10048}=\sqrt{64*157}=\sqrt{64}*\sqrt{157}=8\sqrt{157}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{157}}{2*16}=\frac{0-8\sqrt{157}}{32}
=-\frac{8\sqrt{157}}{32}
=-\frac{\sqrt{157}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{157}}{2*16}=\frac{0+8\sqrt{157}}{32}
=\frac{8\sqrt{157}}{32}
=\frac{\sqrt{157}}{4}
$