6x-4=-1/6x+5

Solution for 6x-4=-1/6x+5 equation:

6x-4=-1/6x+5

We move all terms to the left:

6x-4-(-1/6x+5)=0


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

x∈R


We get rid of parentheses

6x+1/6x-5-4=0

We multiply all the terms by the denominator


6x*6x-5*6x-4*6x+1=0

Wy multiply elements

36x^2-30x-24x+1=0

We add all the numbers together, and all the variables

36x^2-54x+1=0

a = 36; b = -54; c = +1;
Δ = b2-4ac
Δ = -542-4·36·1
Δ = 2772
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:

$\sqrt{\Delta}=\sqrt{2772}=\sqrt{36*77}=\sqrt{36}*\sqrt{77}=6\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{77}}{2*36}=\frac{54-6\sqrt{77}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{77}}{2*36}=\frac{54+6\sqrt{77}}{72}
$