5/9x+8=-x-6

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

5/9x+8=-x-6

We move all terms to the left:

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


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

5/9x-(-1x-6)+8=0

We get rid of parentheses

5/9x+1x+6+8=0

We multiply all the terms by the denominator


1x*9x+6*9x+8*9x+5=0

Wy multiply elements

9x^2+54x+72x+5=0

We add all the numbers together, and all the variables

9x^2+126x+5=0

a = 9; b = 126; c = +5;
Δ = b2-4ac
Δ = 1262-4·9·5
Δ = 15696
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:

$\sqrt{\Delta}=\sqrt{15696}=\sqrt{144*109}=\sqrt{144}*\sqrt{109}=12\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-12\sqrt{109}}{2*9}=\frac{-126-12\sqrt{109}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+12\sqrt{109}}{2*9}=\frac{-126+12\sqrt{109}}{18}
$