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

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

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

We move all terms to the left:

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


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

8/9x+5/6x-6=0

We calculate fractions


48x/54x^2+45x/54x^2-6=0

We multiply all the terms by the denominator


48x+45x-6*54x^2=0

We add all the numbers together, and all the variables

93x-6*54x^2=0

Wy multiply elements

-324x^2+93x=0

a = -324; b = 93; c = 0;
Δ = b2-4ac
Δ = 932-4·(-324)·0
Δ = 8649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8649}=93$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(93)-93}{2*-324}=\frac{-186}{-648}
=31/108
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(93)+93}{2*-324}=\frac{0}{-648}
=0
$