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

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

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

We move all terms to the left:

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


Domain of the equation: 2x+15)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


2x*2x+x*2x-120*2x-30*2x+15*2x-180*2x+1=0

Wy multiply elements

4x^2+2x^2-240x-60x+30x-360x+1=0

We add all the numbers together, and all the variables

6x^2-630x+1=0

a = 6; b = -630; c = +1;
Δ = b2-4ac
Δ = -6302-4·6·1
Δ = 396876
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:

$\sqrt{\Delta}=\sqrt{396876}=\sqrt{4*99219}=\sqrt{4}*\sqrt{99219}=2\sqrt{99219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-630)-2\sqrt{99219}}{2*6}=\frac{630-2\sqrt{99219}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-630)+2\sqrt{99219}}{2*6}=\frac{630+2\sqrt{99219}}{12}
$