150-x+3x+1/5x+19=180

Solution for 150-x+3x+1/5x+19=180 equation:

150-x+3x+1/5x+19=180

We move all terms to the left:

150-x+3x+1/5x+19-(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+1/5x-11=0

We multiply all the terms by the denominator


2x*5x-11*5x+1=0

Wy multiply elements

10x^2-55x+1=0

a = 10; b = -55; c = +1;
Δ = b2-4ac
Δ = -552-4·10·1
Δ = 2985
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-\sqrt{2985}}{2*10}=\frac{55-\sqrt{2985}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+\sqrt{2985}}{2*10}=\frac{55+\sqrt{2985}}{20}
$