1/2x+30x=180

Solution for 1/2x+30x=180 equation:

1/2x+30x=180

We move all terms to the left:

1/2x+30x-(180)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

30x+1/2x-180=0

We multiply all the terms by the denominator


30x*2x-180*2x+1=0

Wy multiply elements

60x^2-360x+1=0

a = 60; b = -360; c = +1;
Δ = b2-4ac
Δ = -3602-4·60·1
Δ = 129360
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:

$\sqrt{\Delta}=\sqrt{129360}=\sqrt{784*165}=\sqrt{784}*\sqrt{165}=28\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-28\sqrt{165}}{2*60}=\frac{360-28\sqrt{165}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+28\sqrt{165}}{2*60}=\frac{360+28\sqrt{165}}{120}
$