x-30+2x-120+(1/2)x+15=180

Solution for x-30+2x-120+(1/2)x+15=180 equation:

x-30+2x-120+(1/2)x+15=180

We move all terms to the left:

x-30+2x-120+(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

x+2x+(+1/2)x-30-120+15-180=0

We add all the numbers together, and all the variables

3x+(+1/2)x-315=0

We multiply parentheses

x^2+3x-315=0

a = 1; b = 3; c = -315;
Δ = b2-4ac
Δ = 32-4·1·(-315)
Δ = 1269
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:

$\sqrt{\Delta}=\sqrt{1269}=\sqrt{9*141}=\sqrt{9}*\sqrt{141}=3\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{141}}{2*1}=\frac{-3-3\sqrt{141}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{141}}{2*1}=\frac{-3+3\sqrt{141}}{2}
$