6/x=(x-14)/4

Solution for 6/x=(x-14)/4 equation:

6/x=(x-14)/4

We move all terms to the left:

6/x-((x-14)/4)=0


Domain of the equation: x!=0

x∈R


We calculate fractions


()/4x^2+(-((x-14)*x)/4x^2=0

We multiply all the terms by the denominator


(-((x-14)*x)+()=0


We calculate terms in parentheses: +(-((x-14)*x)+(), so:

-((x-14)*x)+(

We add all the numbers together, and all the variables

-((x-14)*x)


We calculate terms in parentheses: -((x-14)*x), so:

(x-14)*x

We multiply parentheses

x^2-14x

Back to the equation:

-(x^2-14x)


We get rid of parentheses

-x^2+14x

We add all the numbers together, and all the variables

-1x^2+14x

Back to the equation:

+(-1x^2+14x)


We get rid of parentheses

-1x^2+14x=0

a = -1; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-1)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-1}=\frac{-28}{-2}
=+14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-1}=\frac{0}{-2}
=0
$