8/9x=x-5

Solution for 8/9x=x-5 equation:

8/9x=x-5

We move all terms to the left:

8/9x-(x-5)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We get rid of parentheses

8/9x-x+5=0

We multiply all the terms by the denominator


-x*9x+5*9x+8=0

Wy multiply elements

-9x^2+45x+8=0

a = -9; b = 45; c = +8;
Δ = b2-4ac
Δ = 452-4·(-9)·8
Δ = 2313
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:

$\sqrt{\Delta}=\sqrt{2313}=\sqrt{9*257}=\sqrt{9}*\sqrt{257}=3\sqrt{257}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{257}}{2*-9}=\frac{-45-3\sqrt{257}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{257}}{2*-9}=\frac{-45+3\sqrt{257}}{-18}
$