2+x=157/8x

Solution for 2+x=157/8x equation:

2+x=157/8x

We move all terms to the left:

2+x-(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

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

We get rid of parentheses

x-157/8x+2=0

We multiply all the terms by the denominator


x*8x+2*8x-157=0

Wy multiply elements

8x^2+16x-157=0

a = 8; b = 16; c = -157;
Δ = b2-4ac
Δ = 162-4·8·(-157)
Δ = 5280
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:

$\sqrt{\Delta}=\sqrt{5280}=\sqrt{16*330}=\sqrt{16}*\sqrt{330}=4\sqrt{330}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{330}}{2*8}=\frac{-16-4\sqrt{330}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{330}}{2*8}=\frac{-16+4\sqrt{330}}{16}
$