(1/2x+39)+x=180

Solution for (1/2x+39)+x=180 equation:

(1/2x+39)+x=180

We move all terms to the left:

(1/2x+39)+x-(180)=0


Domain of the equation: 2x+39)!=0

x∈R


We add all the numbers together, and all the variables

x+(1/2x+39)-180=0

We get rid of parentheses

x+1/2x+39-180=0

We multiply all the terms by the denominator


x*2x+39*2x-180*2x+1=0

Wy multiply elements

2x^2+78x-360x+1=0

We add all the numbers together, and all the variables

2x^2-282x+1=0

a = 2; b = -282; c = +1;
Δ = b2-4ac
Δ = -2822-4·2·1
Δ = 79516
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:

$\sqrt{\Delta}=\sqrt{79516}=\sqrt{4*19879}=\sqrt{4}*\sqrt{19879}=2\sqrt{19879}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-282)-2\sqrt{19879}}{2*2}=\frac{282-2\sqrt{19879}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-282)+2\sqrt{19879}}{2*2}=\frac{282+2\sqrt{19879}}{4}
$