(X-26)+(2x-80)+(1/2x+13)=180

Solution for (X-26)+(2x-80)+(1/2x+13)=180 equation:

(X-26)+(2X-80)+(1/2X+13)=180

We move all terms to the left:

(X-26)+(2X-80)+(1/2X+13)-(180)=0


Domain of the equation: 2X+13)!=0

X∈R


We get rid of parentheses

X+2X+1/2X-26-80+13-180=0

We multiply all the terms by the denominator


X*2X+2X*2X-26*2X-80*2X+13*2X-180*2X+1=0

Wy multiply elements

2X^2+4X^2-52X-160X+26X-360X+1=0

We add all the numbers together, and all the variables

6X^2-546X+1=0

a = 6; b = -546; c = +1;
Δ = b2-4ac
Δ = -5462-4·6·1
Δ = 298092
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:

$\sqrt{\Delta}=\sqrt{298092}=\sqrt{4*74523}=\sqrt{4}*\sqrt{74523}=2\sqrt{74523}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-546)-2\sqrt{74523}}{2*6}=\frac{546-2\sqrt{74523}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-546)+2\sqrt{74523}}{2*6}=\frac{546+2\sqrt{74523}}{12}
$