(7/12)x=3/14

Solution for (7/12)x=3/14 equation:

(7/12)x=3/14

We move all terms to the left:

(7/12)x-(3/14)=0


Domain of the equation: 12)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+7/12)x-(+3/14)=0

We multiply parentheses

7x^2-(+3/14)=0

We get rid of parentheses

7x^2-3/14=0

We multiply all the terms by the denominator


7x^2*14-3=0

Wy multiply elements

98x^2-3=0

a = 98; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·98·(-3)
Δ = 1176
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:

$\sqrt{\Delta}=\sqrt{1176}=\sqrt{196*6}=\sqrt{196}*\sqrt{6}=14\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{6}}{2*98}=\frac{0-14\sqrt{6}}{196}
=-\frac{14\sqrt{6}}{196}
=-\frac{\sqrt{6}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{6}}{2*98}=\frac{0+14\sqrt{6}}{196}
=\frac{14\sqrt{6}}{196}
=\frac{\sqrt{6}}{14}
$