x-6+1/5x=180

Solution for x-6+1/5x=180 equation:

x-6+1/5x=180

We move all terms to the left:

x-6+1/5x-(180)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/5x-186=0

We multiply all the terms by the denominator


x*5x-186*5x+1=0

Wy multiply elements

5x^2-930x+1=0

a = 5; b = -930; c = +1;
Δ = b2-4ac
Δ = -9302-4·5·1
Δ = 864880
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:

$\sqrt{\Delta}=\sqrt{864880}=\sqrt{16*54055}=\sqrt{16}*\sqrt{54055}=4\sqrt{54055}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-930)-4\sqrt{54055}}{2*5}=\frac{930-4\sqrt{54055}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-930)+4\sqrt{54055}}{2*5}=\frac{930+4\sqrt{54055}}{10}
$