5-(x+4)+6/6=-(x-8)+4/9

Solution for 5-(x+4)+6/6=-(x-8)+4/9 equation:

5-(x+4)+6/6=-(x-8)+4/9

We move all terms to the left:

5-(x+4)+6/6-(-(x-8)+4/9)=0

We add all the numbers together, and all the variables

-(x+4)-(-(x-8)+4/9)+6=0

We get rid of parentheses

-x-(-(x-8)+4/9)-4+6=0

We multiply all the terms by the denominator


-x*9)-(-(x-8)+4-4*9)+6*9)=0

We add all the numbers together, and all the variables

-x*9)-(-(x-8)=0

Wy multiply elements

-9x^2-(x-8)=0

We get rid of parentheses

-9x^2-x+8=0

We add all the numbers together, and all the variables

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

a = -9; b = -1; c = +8;
Δ = b2-4ac
Δ = -12-4·(-9)·8
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-17}{2*-9}=\frac{-16}{-18}
=8/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+17}{2*-9}=\frac{18}{-18}
=-1
$