3x+1/2x=180

Solution for 3x+1/2x=180 equation:

3x+1/2x=180

We move all terms to the left:

3x+1/2x-(180)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


3x*2x-180*2x+1=0

Wy multiply elements

6x^2-360x+1=0

a = 6; b = -360; c = +1;
Δ = b2-4ac
Δ = -3602-4·6·1
Δ = 129576
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:

$\sqrt{\Delta}=\sqrt{129576}=\sqrt{4*32394}=\sqrt{4}*\sqrt{32394}=2\sqrt{32394}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-2\sqrt{32394}}{2*6}=\frac{360-2\sqrt{32394}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+2\sqrt{32394}}{2*6}=\frac{360+2\sqrt{32394}}{12}
$