2/3x-8+5/6x-5=23

Solution for 2/3x-8+5/6x-5=23 equation:

2/3x-8+5/6x-5=23

We move all terms to the left:

2/3x-8+5/6x-5-(23)=0


Domain of the equation: 3x!=0

x!=0/3

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

2/3x+5/6x-36=0

We calculate fractions


12x/18x^2+15x/18x^2-36=0

We multiply all the terms by the denominator


12x+15x-36*18x^2=0

We add all the numbers together, and all the variables

27x-36*18x^2=0

Wy multiply elements

-648x^2+27x=0

a = -648; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-648)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-648}=\frac{-54}{-1296}
=1/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-648}=\frac{0}{-1296}
=0
$