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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

X^2+X^2+X^2+2X-99=0

We add all the numbers together, and all the variables

3X^2+2X-99=0

a = 3; b = 2; c = -99;
Δ = b2-4ac
Δ = 22-4·3·(-99)
Δ = 1192
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:

$\sqrt{\Delta}=\sqrt{1192}=\sqrt{4*298}=\sqrt{4}*\sqrt{298}=2\sqrt{298}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{298}}{2*3}=\frac{-2-2\sqrt{298}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{298}}{2*3}=\frac{-2+2\sqrt{298}}{6}
$