6x=5/6x+36

Solution for 6x=5/6x+36 equation:

6x=5/6x+36

We move all terms to the left:

6x-(5/6x+36)=0


Domain of the equation: 6x+36)!=0

x∈R


We get rid of parentheses

6x-5/6x-36=0

We multiply all the terms by the denominator


6x*6x-36*6x-5=0

Wy multiply elements

36x^2-216x-5=0

a = 36; b = -216; c = -5;
Δ = b2-4ac
Δ = -2162-4·36·(-5)
Δ = 47376
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:

$\sqrt{\Delta}=\sqrt{47376}=\sqrt{144*329}=\sqrt{144}*\sqrt{329}=12\sqrt{329}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-12\sqrt{329}}{2*36}=\frac{216-12\sqrt{329}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+12\sqrt{329}}{2*36}=\frac{216+12\sqrt{329}}{72}
$