x-30+2x-92+1/2x+15=180

Solution for x-30+2x-92+1/2x+15=180 equation:

x-30+2x-92+1/2x+15=180

We move all terms to the left:

x-30+2x-92+1/2x+15-(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-287=0

We multiply all the terms by the denominator


3x*2x-287*2x+1=0

Wy multiply elements

6x^2-574x+1=0

a = 6; b = -574; c = +1;
Δ = b2-4ac
Δ = -5742-4·6·1
Δ = 329452
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:

$\sqrt{\Delta}=\sqrt{329452}=\sqrt{4*82363}=\sqrt{4}*\sqrt{82363}=2\sqrt{82363}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-574)-2\sqrt{82363}}{2*6}=\frac{574-2\sqrt{82363}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-574)+2\sqrt{82363}}{2*6}=\frac{574+2\sqrt{82363}}{12}
$