(5/6)x=5/14

Solution for (5/6)x=5/14 equation:

(5/6)x=5/14

We move all terms to the left:

(5/6)x-(5/14)=0


Domain of the equation: 6)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+5/6)x-(+5/14)=0

We multiply parentheses

5x^2-(+5/14)=0

We get rid of parentheses

5x^2-5/14=0

We multiply all the terms by the denominator


5x^2*14-5=0

Wy multiply elements

70x^2-5=0

a = 70; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·70·(-5)
Δ = 1400
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:

$\sqrt{\Delta}=\sqrt{1400}=\sqrt{100*14}=\sqrt{100}*\sqrt{14}=10\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{14}}{2*70}=\frac{0-10\sqrt{14}}{140}
=-\frac{10\sqrt{14}}{140}
=-\frac{\sqrt{14}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{14}}{2*70}=\frac{0+10\sqrt{14}}{140}
=\frac{10\sqrt{14}}{140}
=\frac{\sqrt{14}}{14}
$