(X-35)+x+(x-46)+(1/2)x=360

Solution for (X-35)+x+(x-46)+(1/2)x=360 equation:

(X-35)+X+(X-46)+(1/2)X=360

We move all terms to the left:

(X-35)+X+(X-46)+(1/2)X-(360)=0


Domain of the equation: 2)X!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

(X-35)+X+(X-46)+(+1/2)X-360=0

We add all the numbers together, and all the variables

X+(X-35)+(X-46)+(+1/2)X-360=0

We multiply parentheses

X^2+X+(X-35)+(X-46)-360=0

We get rid of parentheses

X^2+X+X+X-35-46-360=0

We add all the numbers together, and all the variables

X^2+3X-441=0

a = 1; b = 3; c = -441;
Δ = b2-4ac
Δ = 32-4·1·(-441)
Δ = 1773
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:

$\sqrt{\Delta}=\sqrt{1773}=\sqrt{9*197}=\sqrt{9}*\sqrt{197}=3\sqrt{197}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{197}}{2*1}=\frac{-3-3\sqrt{197}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{197}}{2*1}=\frac{-3+3\sqrt{197}}{2}
$