7x=3/8,x

Solution for 7x=3/8,x equation:

7x=3/8.x

We move all terms to the left:

7x-(3/8.x)=0


Domain of the equation: 8.x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7x-(+3/8.x)=0

We get rid of parentheses

7x-3/8.x=0

We multiply all the terms by the denominator


7x*8.x-3=0

Wy multiply elements

56x^2-3=0

a = 56; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·56·(-3)
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*56}=\frac{0-4\sqrt{42}}{112}
=-\frac{4\sqrt{42}}{112}
=-\frac{\sqrt{42}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{42}}{2*56}=\frac{0+4\sqrt{42}}{112}
=\frac{4\sqrt{42}}{112}
=\frac{\sqrt{42}}{28}
$