X+1/2x+2=40

Solution for X+1/2x+2=40 equation:

X+1/2X+2=40

We move all terms to the left:

X+1/2X+2-(40)=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-38=0

We multiply all the terms by the denominator


X*2X-38*2X+1=0

Wy multiply elements

2X^2-76X+1=0

a = 2; b = -76; c = +1;
Δ = b2-4ac
Δ = -762-4·2·1
Δ = 5768
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:

$\sqrt{\Delta}=\sqrt{5768}=\sqrt{4*1442}=\sqrt{4}*\sqrt{1442}=2\sqrt{1442}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-2\sqrt{1442}}{2*2}=\frac{76-2\sqrt{1442}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+2\sqrt{1442}}{2*2}=\frac{76+2\sqrt{1442}}{4}
$