7x+7/9x=-42

Solution for 7x+7/9x=-42 equation:

7x+7/9x=-42

We move all terms to the left:

7x+7/9x-(-42)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

7x+7/9x+42=0

We multiply all the terms by the denominator


7x*9x+42*9x+7=0

Wy multiply elements

63x^2+378x+7=0

a = 63; b = 378; c = +7;
Δ = b2-4ac
Δ = 3782-4·63·7
Δ = 141120
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:

$\sqrt{\Delta}=\sqrt{141120}=\sqrt{28224*5}=\sqrt{28224}*\sqrt{5}=168\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(378)-168\sqrt{5}}{2*63}=\frac{-378-168\sqrt{5}}{126}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(378)+168\sqrt{5}}{2*63}=\frac{-378+168\sqrt{5}}{126}
$