7/9x=x-40

Solution for 7/9x=x-40 equation:

7/9x=x-40

We move all terms to the left:

7/9x-(x-40)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We get rid of parentheses

7/9x-x+40=0

We multiply all the terms by the denominator


-x*9x+40*9x+7=0

Wy multiply elements

-9x^2+360x+7=0

a = -9; b = 360; c = +7;
Δ = b2-4ac
Δ = 3602-4·(-9)·7
Δ = 129852
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:

$\sqrt{\Delta}=\sqrt{129852}=\sqrt{36*3607}=\sqrt{36}*\sqrt{3607}=6\sqrt{3607}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-6\sqrt{3607}}{2*-9}=\frac{-360-6\sqrt{3607}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+6\sqrt{3607}}{2*-9}=\frac{-360+6\sqrt{3607}}{-18}
$