4x+6=660/x

Solution for 4x+6=660/x equation:

4x+6=660/x

We move all terms to the left:

4x+6-(660/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x-(+660/x)+6=0

We get rid of parentheses

4x-660/x+6=0

We multiply all the terms by the denominator


4x*x+6*x-660=0

We add all the numbers together, and all the variables

6x+4x*x-660=0

Wy multiply elements

4x^2+6x-660=0

a = 4; b = 6; c = -660;
Δ = b2-4ac
Δ = 62-4·4·(-660)
Δ = 10596
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:

$\sqrt{\Delta}=\sqrt{10596}=\sqrt{4*2649}=\sqrt{4}*\sqrt{2649}=2\sqrt{2649}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{2649}}{2*4}=\frac{-6-2\sqrt{2649}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{2649}}{2*4}=\frac{-6+2\sqrt{2649}}{8}
$