2x-40+1/2x+20+2x-115=180

Solution for 2x-40+1/2x+20+2x-115=180 equation:

2x-40+1/2x+20+2x-115=180

We move all terms to the left:

2x-40+1/2x+20+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

4x+1/2x-315=0

We multiply all the terms by the denominator


4x*2x-315*2x+1=0

Wy multiply elements

8x^2-630x+1=0

a = 8; b = -630; c = +1;
Δ = b2-4ac
Δ = -6302-4·8·1
Δ = 396868
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:

$\sqrt{\Delta}=\sqrt{396868}=\sqrt{4*99217}=\sqrt{4}*\sqrt{99217}=2\sqrt{99217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-630)-2\sqrt{99217}}{2*8}=\frac{630-2\sqrt{99217}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-630)+2\sqrt{99217}}{2*8}=\frac{630+2\sqrt{99217}}{16}
$