(X+30)+(3x-30)+(1/2x+45)=180

Solution for (X+30)+(3x-30)+(1/2x+45)=180 equation:

(X+30)+(3X-30)+(1/2X+45)=180

We move all terms to the left:

(X+30)+(3X-30)+(1/2X+45)-(180)=0


Domain of the equation: 2X+45)!=0

X∈R


We get rid of parentheses

X+3X+1/2X+30-30+45-180=0

We multiply all the terms by the denominator


X*2X+3X*2X+30*2X-30*2X+45*2X-180*2X+1=0

Wy multiply elements

2X^2+6X^2+60X-60X+90X-360X+1=0

We add all the numbers together, and all the variables

8X^2-270X+1=0

a = 8; b = -270; c = +1;
Δ = b2-4ac
Δ = -2702-4·8·1
Δ = 72868
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:

$\sqrt{\Delta}=\sqrt{72868}=\sqrt{4*18217}=\sqrt{4}*\sqrt{18217}=2\sqrt{18217}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-2\sqrt{18217}}{2*8}=\frac{270-2\sqrt{18217}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+2\sqrt{18217}}{2*8}=\frac{270+2\sqrt{18217}}{16}
$