1/2x+x+(X+5)=100

Solution for 1/2x+x+(X+5)=100 equation:

1/2x+x+(x+5)=100

We move all terms to the left:

1/2x+x+(x+5)-(100)=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+(x+5)-100=0

We get rid of parentheses

x+1/2x+x+5-100=0

We multiply all the terms by the denominator


x*2x+x*2x+5*2x-100*2x+1=0

Wy multiply elements

2x^2+2x^2+10x-200x+1=0

We add all the numbers together, and all the variables

4x^2-190x+1=0

a = 4; b = -190; c = +1;
Δ = b2-4ac
Δ = -1902-4·4·1
Δ = 36084
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:

$\sqrt{\Delta}=\sqrt{36084}=\sqrt{4*9021}=\sqrt{4}*\sqrt{9021}=2\sqrt{9021}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-190)-2\sqrt{9021}}{2*4}=\frac{190-2\sqrt{9021}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-190)+2\sqrt{9021}}{2*4}=\frac{190+2\sqrt{9021}}{8}
$