1/2x+(x-35)+(x-40)+x=360

Solution for 1/2x+(x-35)+(x-40)+x=360 equation:

1/2x+(x-35)+(x-40)+x=360

We move all terms to the left:

1/2x+(x-35)+(x-40)+x-(360)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/2x+(x-35)+(x-40)-360=0

We get rid of parentheses

x+1/2x+x+x-35-40-360=0

We multiply all the terms by the denominator


x*2x+x*2x+x*2x-35*2x-40*2x-360*2x+1=0

Wy multiply elements

2x^2+2x^2+2x^2-70x-80x-720x+1=0

We add all the numbers together, and all the variables

6x^2-870x+1=0

a = 6; b = -870; c = +1;
Δ = b2-4ac
Δ = -8702-4·6·1
Δ = 756876
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:

$\sqrt{\Delta}=\sqrt{756876}=\sqrt{4*189219}=\sqrt{4}*\sqrt{189219}=2\sqrt{189219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-870)-2\sqrt{189219}}{2*6}=\frac{870-2\sqrt{189219}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-870)+2\sqrt{189219}}{2*6}=\frac{870+2\sqrt{189219}}{12}
$