3/5x+2x=180

Solution for 3/5x+2x=180 equation:

3/5x+2x=180

We move all terms to the left:

3/5x+2x-(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

2x+3/5x-180=0

We multiply all the terms by the denominator


2x*5x-180*5x+3=0

Wy multiply elements

10x^2-900x+3=0

a = 10; b = -900; c = +3;
Δ = b2-4ac
Δ = -9002-4·10·3
Δ = 809880
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:

$\sqrt{\Delta}=\sqrt{809880}=\sqrt{4*202470}=\sqrt{4}*\sqrt{202470}=2\sqrt{202470}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-900)-2\sqrt{202470}}{2*10}=\frac{900-2\sqrt{202470}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-900)+2\sqrt{202470}}{2*10}=\frac{900+2\sqrt{202470}}{20}
$