(1/16)x-2=5/8

Solution for (1/16)x-2=5/8 equation:

(1/16)x-2=5/8

We move all terms to the left:

(1/16)x-2-(5/8)=0


Domain of the equation: 16)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/16)x-2-(+5/8)=0

We multiply parentheses

x^2-2-(+5/8)=0

We get rid of parentheses

x^2-2-5/8=0

We multiply all the terms by the denominator


x^2*8-5-2*8=0

We add all the numbers together, and all the variables

x^2*8-21=0

Wy multiply elements

8x^2-21=0

a = 8; b = 0; c = -21;
Δ = b2-4ac
Δ = 02-4·8·(-21)
Δ = 672
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:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{42}}{2*8}=\frac{0-4\sqrt{42}}{16}
=-\frac{4\sqrt{42}}{16}
=-\frac{\sqrt{42}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{42}}{2*8}=\frac{0+4\sqrt{42}}{16}
=\frac{4\sqrt{42}}{16}
=\frac{\sqrt{42}}{4}
$