x+18/4x=180

Solution for x+18/4x=180 equation:

x+18/4x=180

We move all terms to the left:

x+18/4x-(180)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


x*4x-180*4x+18=0

Wy multiply elements

4x^2-720x+18=0

a = 4; b = -720; c = +18;
Δ = b2-4ac
Δ = -7202-4·4·18
Δ = 518112
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:

$\sqrt{\Delta}=\sqrt{518112}=\sqrt{144*3598}=\sqrt{144}*\sqrt{3598}=12\sqrt{3598}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-720)-12\sqrt{3598}}{2*4}=\frac{720-12\sqrt{3598}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-720)+12\sqrt{3598}}{2*4}=\frac{720+12\sqrt{3598}}{8}
$