1/2x+14-9/x+7=-6

Solution for 1/2x+14-9/x+7=-6 equation:

1/2x+14-9/x+7=-6

We move all terms to the left:

1/2x+14-9/x+7-(-6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-9/x+27=0

We calculate fractions


x/2x^2+(-18x)/2x^2+27=0

We multiply all the terms by the denominator


x+(-18x)+27*2x^2=0

Wy multiply elements

54x^2+x+(-18x)=0

We get rid of parentheses

54x^2+x-18x=0

We add all the numbers together, and all the variables

54x^2-17x=0

a = 54; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·54·0
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{-(-17)-17}{2*54}=\frac{0}{108}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*54}=\frac{34}{108}
=17/54
$