70/x-9=x

Solution for 70/x-9=x equation:

70/x-9=x

We move all terms to the left:

70/x-9-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1x+70/x-9=0

We multiply all the terms by the denominator


-1x*x-9*x+70=0

We add all the numbers together, and all the variables

-9x-1x*x+70=0

Wy multiply elements

-1x^2-9x+70=0

a = -1; b = -9; c = +70;
Δ = b2-4ac
Δ = -92-4·(-1)·70
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-19}{2*-1}=\frac{-10}{-2}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+19}{2*-1}=\frac{28}{-2}
=-14
$