(x-35)+(x-42)+x+1/2x=360

Solution for (x-35)+(x-42)+x+1/2x=360 equation:

(x-35)+(x-42)+x+1/2x=360

We move all terms to the left:

(x-35)+(x-42)+x+1/2x-(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+(x-35)+(x-42)+1/2x-360=0

We get rid of parentheses

x+x+x+1/2x-35-42-360=0

We multiply all the terms by the denominator


x*2x+x*2x+x*2x-35*2x-42*2x-360*2x+1=0

Wy multiply elements

2x^2+2x^2+2x^2-70x-84x-720x+1=0

We add all the numbers together, and all the variables

6x^2-874x+1=0

a = 6; b = -874; c = +1;
Δ = b2-4ac
Δ = -8742-4·6·1
Δ = 763852
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:

$\sqrt{\Delta}=\sqrt{763852}=\sqrt{4*190963}=\sqrt{4}*\sqrt{190963}=2\sqrt{190963}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-874)-2\sqrt{190963}}{2*6}=\frac{874-2\sqrt{190963}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-874)+2\sqrt{190963}}{2*6}=\frac{874+2\sqrt{190963}}{12}
$