x-10+1/2x+5+2x-30=180

Solution for x-10+1/2x+5+2x-30=180 equation:

x-10+1/2x+5+2x-30=180

We move all terms to the left:

x-10+1/2x+5+2x-30-(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-215=0

We multiply all the terms by the denominator


3x*2x-215*2x+1=0

Wy multiply elements

6x^2-430x+1=0

a = 6; b = -430; c = +1;
Δ = b2-4ac
Δ = -4302-4·6·1
Δ = 184876
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:

$\sqrt{\Delta}=\sqrt{184876}=\sqrt{4*46219}=\sqrt{4}*\sqrt{46219}=2\sqrt{46219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-430)-2\sqrt{46219}}{2*6}=\frac{430-2\sqrt{46219}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-430)+2\sqrt{46219}}{2*6}=\frac{430+2\sqrt{46219}}{12}
$