X+1/2x+1/2x-5=35

Solution for X+1/2x+1/2x-5=35 equation:

X+1/2X+1/2X-5=35

We move all terms to the left:

X+1/2X+1/2X-5-(35)=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+1/2X-40=0

We multiply all the terms by the denominator


X*2X-40*2X+1+1=0

We add all the numbers together, and all the variables

X*2X-40*2X+2=0

Wy multiply elements

2X^2-80X+2=0

a = 2; b = -80; c = +2;
Δ = b2-4ac
Δ = -802-4·2·2
Δ = 6384
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:

$\sqrt{\Delta}=\sqrt{6384}=\sqrt{16*399}=\sqrt{16}*\sqrt{399}=4\sqrt{399}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{399}}{2*2}=\frac{80-4\sqrt{399}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{399}}{2*2}=\frac{80+4\sqrt{399}}{4}
$