2x-8=5/6x+5

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

2x-8=5/6x+5

We move all terms to the left:

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


Domain of the equation: 6x+5)!=0

x∈R


We get rid of parentheses

2x-5/6x-5-8=0

We multiply all the terms by the denominator


2x*6x-5*6x-8*6x-5=0

Wy multiply elements

12x^2-30x-48x-5=0

We add all the numbers together, and all the variables

12x^2-78x-5=0

a = 12; b = -78; c = -5;
Δ = b2-4ac
Δ = -782-4·12·(-5)
Δ = 6324
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:

$\sqrt{\Delta}=\sqrt{6324}=\sqrt{4*1581}=\sqrt{4}*\sqrt{1581}=2\sqrt{1581}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{1581}}{2*12}=\frac{78-2\sqrt{1581}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{1581}}{2*12}=\frac{78+2\sqrt{1581}}{24}
$