x-2/9x=140

Solution for x-2/9x=140 equation:

x-2/9x=140

We move all terms to the left:

x-2/9x-(140)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We multiply all the terms by the denominator


x*9x-140*9x-2=0

Wy multiply elements

9x^2-1260x-2=0

a = 9; b = -1260; c = -2;
Δ = b2-4ac
Δ = -12602-4·9·(-2)
Δ = 1587672
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:

$\sqrt{\Delta}=\sqrt{1587672}=\sqrt{36*44102}=\sqrt{36}*\sqrt{44102}=6\sqrt{44102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1260)-6\sqrt{44102}}{2*9}=\frac{1260-6\sqrt{44102}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1260)+6\sqrt{44102}}{2*9}=\frac{1260+6\sqrt{44102}}{18}
$