(4/7)x=6/7

Solution for (4/7)x=6/7 equation:

(4/7)x=6/7

We move all terms to the left:

(4/7)x-(6/7)=0


Domain of the equation: 7)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+4/7)x-(+6/7)=0

We multiply parentheses

4x^2-(+6/7)=0

We get rid of parentheses

4x^2-6/7=0

We multiply all the terms by the denominator


4x^2*7-6=0

Wy multiply elements

28x^2-6=0

a = 28; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·28·(-6)
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*28}=\frac{0-4\sqrt{42}}{56}
=-\frac{4\sqrt{42}}{56}
=-\frac{\sqrt{42}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{42}}{2*28}=\frac{0+4\sqrt{42}}{56}
=\frac{4\sqrt{42}}{56}
=\frac{\sqrt{42}}{14}
$