66.6x+4=1/6x-5

Solution for 66.6x+4=1/6x-5 equation:

66.6x+4=1/6x-5

We move all terms to the left:

66.6x+4-(1/6x-5)=0


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

x∈R


We get rid of parentheses

66.6x-1/6x+5+4=0

We multiply all the terms by the denominator


(66.6x)*6x+5*6x+4*6x-1=0

We add all the numbers together, and all the variables

(+66.6x)*6x+5*6x+4*6x-1=0

We multiply parentheses

396x^2+5*6x+4*6x-1=0

Wy multiply elements

396x^2+30x+24x-1=0

We add all the numbers together, and all the variables

396x^2+54x-1=0

a = 396; b = 54; c = -1;
Δ = b2-4ac
Δ = 542-4·396·(-1)
Δ = 4500
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:

$\sqrt{\Delta}=\sqrt{4500}=\sqrt{900*5}=\sqrt{900}*\sqrt{5}=30\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-30\sqrt{5}}{2*396}=\frac{-54-30\sqrt{5}}{792}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+30\sqrt{5}}{2*396}=\frac{-54+30\sqrt{5}}{792}
$