x+x*2+(1/2)x+(1/4)x+1=100

Solution for x+x*2+(1/2)x+(1/4)x+1=100 equation:

x+x*2+(1/2)x+(1/4)x+1=100

We move all terms to the left:

x+x*2+(1/2)x+(1/4)x+1-(100)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+x*2+(+1/2)x+(+1/4)x+1-100=0

We add all the numbers together, and all the variables

x+x*2+(+1/2)x+(+1/4)x-99=0

We multiply parentheses

x^2+x^2+x+x*2-99=0

Wy multiply elements

x^2+x^2+x+2x-99=0

We add all the numbers together, and all the variables

2x^2+3x-99=0

a = 2; b = 3; c = -99;
Δ = b2-4ac
Δ = 32-4·2·(-99)
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{89}}{2*2}=\frac{-3-3\sqrt{89}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{89}}{2*2}=\frac{-3+3\sqrt{89}}{4}
$