x-28+2x-107+1/2x+14=180

Solution for x-28+2x-107+1/2x+14=180 equation:

x-28+2x-107+1/2x+14=180

We move all terms to the left:

x-28+2x-107+1/2x+14-(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-301=0

We multiply all the terms by the denominator


3x*2x-301*2x+1=0

Wy multiply elements

6x^2-602x+1=0

a = 6; b = -602; c = +1;
Δ = b2-4ac
Δ = -6022-4·6·1
Δ = 362380
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:

$\sqrt{\Delta}=\sqrt{362380}=\sqrt{4*90595}=\sqrt{4}*\sqrt{90595}=2\sqrt{90595}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-602)-2\sqrt{90595}}{2*6}=\frac{602-2\sqrt{90595}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-602)+2\sqrt{90595}}{2*6}=\frac{602+2\sqrt{90595}}{12}
$