X-40+1/2x+2x-115=180

Solution for X-40+1/2x+2x-115=180 equation:

X-40+1/2X+2X-115=180

We move all terms to the left:

X-40+1/2X+2X-115-(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-335=0

We multiply all the terms by the denominator


3X*2X-335*2X+1=0

Wy multiply elements

6X^2-670X+1=0

a = 6; b = -670; c = +1;
Δ = b2-4ac
Δ = -6702-4·6·1
Δ = 448876
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:

$\sqrt{\Delta}=\sqrt{448876}=\sqrt{4*112219}=\sqrt{4}*\sqrt{112219}=2\sqrt{112219}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-670)-2\sqrt{112219}}{2*6}=\frac{670-2\sqrt{112219}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-670)+2\sqrt{112219}}{2*6}=\frac{670+2\sqrt{112219}}{12}
$