2x-120+3x+5+(1/2)x+15=180

Solution for 2x-120+3x+5+(1/2)x+15=180 equation:

2x-120+3x+5+(1/2)x+15=180

We move all terms to the left:

2x-120+3x+5+(1/2)x+15-(180)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x+3x+(+1/2)x-120+5+15-180=0

We add all the numbers together, and all the variables

5x+(+1/2)x-280=0

We multiply parentheses

x^2+5x-280=0

a = 1; b = 5; c = -280;
Δ = b2-4ac
Δ = 52-4·1·(-280)
Δ = 1145
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{-(5)-\sqrt{1145}}{2*1}=\frac{-5-\sqrt{1145}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{1145}}{2*1}=\frac{-5+\sqrt{1145}}{2}
$