8/6x+3/2x=180

Solution for 8/6x+3/2x=180 equation:

8/6x+3/2x=180

We move all terms to the left:

8/6x+3/2x-(180)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


16x/12x^2+18x/12x^2-180=0

We multiply all the terms by the denominator


16x+18x-180*12x^2=0

We add all the numbers together, and all the variables

34x-180*12x^2=0

Wy multiply elements

-2160x^2+34x=0

a = -2160; b = 34; c = 0;
Δ = b2-4ac
Δ = 342-4·(-2160)·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-34}{2*-2160}=\frac{-68}{-4320}
=17/1080
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+34}{2*-2160}=\frac{0}{-4320}
=0
$