8/9x+1=2x-9

Solution for 8/9x+1=2x-9 equation:

8/9x+1=2x-9

We move all terms to the left:

8/9x+1-(2x-9)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We get rid of parentheses

8/9x-2x+9+1=0

We multiply all the terms by the denominator


-2x*9x+9*9x+1*9x+8=0

Wy multiply elements

-18x^2+81x+9x+8=0

We add all the numbers together, and all the variables

-18x^2+90x+8=0

a = -18; b = 90; c = +8;
Δ = b2-4ac
Δ = 902-4·(-18)·8
Δ = 8676
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:

$\sqrt{\Delta}=\sqrt{8676}=\sqrt{36*241}=\sqrt{36}*\sqrt{241}=6\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{241}}{2*-18}=\frac{-90-6\sqrt{241}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{241}}{2*-18}=\frac{-90+6\sqrt{241}}{-36}
$