(1/8)f=5/8

Solution for (1/8)f=5/8 equation:

(1/8)f=5/8

We move all terms to the left:

(1/8)f-(5/8)=0


Domain of the equation: 8)f!=0

f!=0/1

f!=0

f∈R


We add all the numbers together, and all the variables

(+1/8)f-(+5/8)=0

We multiply parentheses

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

We get rid of parentheses

f^2-5/8=0

We multiply all the terms by the denominator


f^2*8-5=0

Wy multiply elements

8f^2-5=0

a = 8; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·8·(-5)
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{10}}{2*8}=\frac{0-4\sqrt{10}}{16}
=-\frac{4\sqrt{10}}{16}
=-\frac{\sqrt{10}}{4}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{10}}{2*8}=\frac{0+4\sqrt{10}}{16}
=\frac{4\sqrt{10}}{16}
=\frac{\sqrt{10}}{4}
$