(68/14)x=63/14

Solution for (68/14)x=63/14 equation:

(68/14)x=63/14

We move all terms to the left:

(68/14)x-(63/14)=0


Domain of the equation: 14)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+68/14)x-(+63/14)=0

We multiply parentheses

68x^2-(+63/14)=0

We get rid of parentheses

68x^2-63/14=0

We multiply all the terms by the denominator


68x^2*14-63=0

Wy multiply elements

952x^2-63=0

a = 952; b = 0; c = -63;
Δ = b2-4ac
Δ = 02-4·952·(-63)
Δ = 239904
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:

$\sqrt{\Delta}=\sqrt{239904}=\sqrt{7056*34}=\sqrt{7056}*\sqrt{34}=84\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-84\sqrt{34}}{2*952}=\frac{0-84\sqrt{34}}{1904}
=-\frac{84\sqrt{34}}{1904}
=-\frac{3\sqrt{34}}{68}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+84\sqrt{34}}{2*952}=\frac{0+84\sqrt{34}}{1904}
=\frac{84\sqrt{34}}{1904}
=\frac{3\sqrt{34}}{68}
$