X+(x-45)+1/2x+(x-35)=360

Solution for X+(x-45)+1/2x+(x-35)=360 equation:

X+(X-45)+1/2X+(X-35)=360

We move all terms to the left:

X+(X-45)+1/2X+(X-35)-(360)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We get rid of parentheses

X+X+1/2X+X-45-35-360=0

We multiply all the terms by the denominator


X*2X+X*2X+X*2X-45*2X-35*2X-360*2X+1=0

Wy multiply elements

2X^2+2X^2+2X^2-90X-70X-720X+1=0

We add all the numbers together, and all the variables

6X^2-880X+1=0

a = 6; b = -880; c = +1;
Δ = b2-4ac
Δ = -8802-4·6·1
Δ = 774376
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:

$\sqrt{\Delta}=\sqrt{774376}=\sqrt{4*193594}=\sqrt{4}*\sqrt{193594}=2\sqrt{193594}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-880)-2\sqrt{193594}}{2*6}=\frac{880-2\sqrt{193594}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-880)+2\sqrt{193594}}{2*6}=\frac{880+2\sqrt{193594}}{12}
$