7/9x+200=x

Solution for 7/9x+200=x equation:

7/9x+200=x

We move all terms to the left:

7/9x+200-(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+7/9x+200=0

We multiply all the terms by the denominator


-1x*9x+200*9x+7=0

Wy multiply elements

-9x^2+1800x+7=0

a = -9; b = 1800; c = +7;
Δ = b2-4ac
Δ = 18002-4·(-9)·7
Δ = 3240252
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:

$\sqrt{\Delta}=\sqrt{3240252}=\sqrt{36*90007}=\sqrt{36}*\sqrt{90007}=6\sqrt{90007}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1800)-6\sqrt{90007}}{2*-9}=\frac{-1800-6\sqrt{90007}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1800)+6\sqrt{90007}}{2*-9}=\frac{-1800+6\sqrt{90007}}{-18}
$