8/9x-2(x+1)=88

Solution for 8/9x-2(x+1)=88 equation:

8/9x-2(x+1)=88

We move all terms to the left:

8/9x-2(x+1)-(88)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We multiply parentheses

8/9x-2x-2-88=0

We multiply all the terms by the denominator


-2x*9x-2*9x-88*9x+8=0

Wy multiply elements

-18x^2-18x-792x+8=0

We add all the numbers together, and all the variables

-18x^2-810x+8=0

a = -18; b = -810; c = +8;
Δ = b2-4ac
Δ = -8102-4·(-18)·8
Δ = 656676
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:

$\sqrt{\Delta}=\sqrt{656676}=\sqrt{36*18241}=\sqrt{36}*\sqrt{18241}=6\sqrt{18241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-810)-6\sqrt{18241}}{2*-18}=\frac{810-6\sqrt{18241}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-810)+6\sqrt{18241}}{2*-18}=\frac{810+6\sqrt{18241}}{-36}
$