7/9x-6=8/11x+5

Solution for 7/9x-6=8/11x+5 equation:

7/9x-6=8/11x+5

We move all terms to the left:

7/9x-6-(8/11x+5)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 11x+5)!=0

x∈R


We get rid of parentheses

7/9x-8/11x-5-6=0

We calculate fractions


77x/99x^2+(-72x)/99x^2-5-6=0

We add all the numbers together, and all the variables

77x/99x^2+(-72x)/99x^2-11=0

We multiply all the terms by the denominator


77x+(-72x)-11*99x^2=0

Wy multiply elements

-1089x^2+77x+(-72x)=0

We get rid of parentheses

-1089x^2+77x-72x=0

We add all the numbers together, and all the variables

-1089x^2+5x=0

a = -1089; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-1089)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-1089}=\frac{-10}{-2178}
=5/1089
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-1089}=\frac{0}{-2178}
=0
$