2x-81+x-10+1/2x+5=180

Solution for 2x-81+x-10+1/2x+5=180 equation:

2x-81+x-10+1/2x+5=180

We move all terms to the left:

2x-81+x-10+1/2x+5-(180)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/2x-266=0

We multiply all the terms by the denominator


3x*2x-266*2x+1=0

Wy multiply elements

6x^2-532x+1=0

a = 6; b = -532; c = +1;
Δ = b2-4ac
Δ = -5322-4·6·1
Δ = 283000
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:

$\sqrt{\Delta}=\sqrt{283000}=\sqrt{100*2830}=\sqrt{100}*\sqrt{2830}=10\sqrt{2830}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-532)-10\sqrt{2830}}{2*6}=\frac{532-10\sqrt{2830}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-532)+10\sqrt{2830}}{2*6}=\frac{532+10\sqrt{2830}}{12}
$