x-2/9x=-7

Solution for x-2/9x=-7 equation:

x-2/9x=-7

We move all terms to the left:

x-2/9x-(-7)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

x-2/9x+7=0

We multiply all the terms by the denominator


x*9x+7*9x-2=0

Wy multiply elements

9x^2+63x-2=0

a = 9; b = 63; c = -2;
Δ = b2-4ac
Δ = 632-4·9·(-2)
Δ = 4041
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:

$\sqrt{\Delta}=\sqrt{4041}=\sqrt{9*449}=\sqrt{9}*\sqrt{449}=3\sqrt{449}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-3\sqrt{449}}{2*9}=\frac{-63-3\sqrt{449}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+3\sqrt{449}}{2*9}=\frac{-63+3\sqrt{449}}{18}
$