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

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

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

We move all terms to the left:

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


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

X∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

2X^2+4X^2-60X+30X-240X-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}
$