5x+1/6x-4=3

Solution for 5x+1/6x-4=3 equation:

5x+1/6x-4=3

We move all terms to the left:

5x+1/6x-4-(3)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

5x+1/6x-7=0

We multiply all the terms by the denominator


5x*6x-7*6x+1=0

Wy multiply elements

30x^2-42x+1=0

a = 30; b = -42; c = +1;
Δ = b2-4ac
Δ = -422-4·30·1
Δ = 1644
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:

$\sqrt{\Delta}=\sqrt{1644}=\sqrt{4*411}=\sqrt{4}*\sqrt{411}=2\sqrt{411}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{411}}{2*30}=\frac{42-2\sqrt{411}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{411}}{2*30}=\frac{42+2\sqrt{411}}{60}
$