10+x+1/2x=180

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

10+x+1/2x=180

We move all terms to the left:

10+x+1/2x-(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

x+1/2x-170=0

We multiply all the terms by the denominator


x*2x-170*2x+1=0

Wy multiply elements

2x^2-340x+1=0

a = 2; b = -340; c = +1;
Δ = b2-4ac
Δ = -3402-4·2·1
Δ = 115592
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:

$\sqrt{\Delta}=\sqrt{115592}=\sqrt{4*28898}=\sqrt{4}*\sqrt{28898}=2\sqrt{28898}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-340)-2\sqrt{28898}}{2*2}=\frac{340-2\sqrt{28898}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-340)+2\sqrt{28898}}{2*2}=\frac{340+2\sqrt{28898}}{4}
$