5x-14/x=6/2

Solution for 5x-14/x=6/2 equation:

5x-14/x=6/2

We move all terms to the left:

5x-14/x-(6/2)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

5x-14/x-3=0

We multiply all the terms by the denominator


5x*x-3*x-14=0

We add all the numbers together, and all the variables

-3x+5x*x-14=0

Wy multiply elements

5x^2-3x-14=0

a = 5; b = -3; c = -14;
Δ = b2-4ac
Δ = -32-4·5·(-14)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-17}{2*5}=\frac{-14}{10}
=-1+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+17}{2*5}=\frac{20}{10}
=2
$