X+1/2x+8=41

Solution for X+1/2x+8=41 equation:

X+1/2X+8=41

We move all terms to the left:

X+1/2X+8-(41)=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-33=0

We multiply all the terms by the denominator


X*2X-33*2X+1=0

Wy multiply elements

2X^2-66X+1=0

a = 2; b = -66; c = +1;
Δ = b2-4ac
Δ = -662-4·2·1
Δ = 4348
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:

$\sqrt{\Delta}=\sqrt{4348}=\sqrt{4*1087}=\sqrt{4}*\sqrt{1087}=2\sqrt{1087}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{1087}}{2*2}=\frac{66-2\sqrt{1087}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{1087}}{2*2}=\frac{66+2\sqrt{1087}}{4}
$