1/2x+4+(1/3x+1)=180

Solution for 1/2x+4+(1/3x+1)=180 equation:

1/2x+4+(1/3x+1)=180

We move all terms to the left:

1/2x+4+(1/3x+1)-(180)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x+1)!=0

x∈R


We add all the numbers together, and all the variables

1/2x+(1/3x+1)-176=0

We get rid of parentheses

1/2x+1/3x+1-176=0

We calculate fractions


3x/6x^2+2x/6x^2+1-176=0

We add all the numbers together, and all the variables

3x/6x^2+2x/6x^2-175=0

We multiply all the terms by the denominator


3x+2x-175*6x^2=0

We add all the numbers together, and all the variables

5x-175*6x^2=0

Wy multiply elements

-1050x^2+5x=0

a = -1050; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-1050)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-1050}=\frac{-10}{-2100}
=1/210
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-1050}=\frac{0}{-2100}
=0
$