x-10+2x-214+1/2x+5=180

Solution for x-10+2x-214+1/2x+5=180 equation:

x-10+2x-214+1/2x+5=180

We move all terms to the left:

x-10+2x-214+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-399=0

We multiply all the terms by the denominator


3x*2x-399*2x+1=0

Wy multiply elements

6x^2-798x+1=0

a = 6; b = -798; c = +1;
Δ = b2-4ac
Δ = -7982-4·6·1
Δ = 636780
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:

$\sqrt{\Delta}=\sqrt{636780}=\sqrt{4*159195}=\sqrt{4}*\sqrt{159195}=2\sqrt{159195}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-798)-2\sqrt{159195}}{2*6}=\frac{798-2\sqrt{159195}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-798)+2\sqrt{159195}}{2*6}=\frac{798+2\sqrt{159195}}{12}
$