4/6x+x=180

Solution for 4/6x+x=180 equation:

4/6x+x=180

We move all terms to the left:

4/6x+x-(180)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

x+4/6x-180=0

We multiply all the terms by the denominator


x*6x-180*6x+4=0

Wy multiply elements

6x^2-1080x+4=0

a = 6; b = -1080; c = +4;
Δ = b2-4ac
Δ = -10802-4·6·4
Δ = 1166304
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:

$\sqrt{\Delta}=\sqrt{1166304}=\sqrt{16*72894}=\sqrt{16}*\sqrt{72894}=4\sqrt{72894}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1080)-4\sqrt{72894}}{2*6}=\frac{1080-4\sqrt{72894}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1080)+4\sqrt{72894}}{2*6}=\frac{1080+4\sqrt{72894}}{12}
$