5/9x+7=x

Solution for 5/9x+7=x equation:

5/9x+7=x

We move all terms to the left:

5/9x+7-(x)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+5/9x+7=0

We multiply all the terms by the denominator


-1x*9x+7*9x+5=0

Wy multiply elements

-9x^2+63x+5=0

a = -9; b = 63; c = +5;
Δ = b2-4ac
Δ = 632-4·(-9)·5
Δ = 4149
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:

$\sqrt{\Delta}=\sqrt{4149}=\sqrt{9*461}=\sqrt{9}*\sqrt{461}=3\sqrt{461}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-3\sqrt{461}}{2*-9}=\frac{-63-3\sqrt{461}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+3\sqrt{461}}{2*-9}=\frac{-63+3\sqrt{461}}{-18}
$