(2/5)x=5/7

Solution for (2/5)x=5/7 equation:

(2/5)x=5/7

We move all terms to the left:

(2/5)x-(5/7)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+2/5)x-(+5/7)=0

We multiply parentheses

2x^2-(+5/7)=0

We get rid of parentheses

2x^2-5/7=0

We multiply all the terms by the denominator


2x^2*7-5=0

Wy multiply elements

14x^2-5=0

a = 14; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·14·(-5)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{70}}{2*14}=\frac{0-2\sqrt{70}}{28}
=-\frac{2\sqrt{70}}{28}
=-\frac{\sqrt{70}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{70}}{2*14}=\frac{0+2\sqrt{70}}{28}
=\frac{2\sqrt{70}}{28}
=\frac{\sqrt{70}}{14}
$