X+x+(1/2)x=21

Solution for X+x+(1/2)x=21 equation:

X+X+(1/2)X=21

We move all terms to the left:

X+X+(1/2)X-(21)=0


Domain of the equation: 2)X!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X+X+(+1/2)X-21=0

We add all the numbers together, and all the variables

2X+(+1/2)X-21=0

We multiply parentheses

X^2+2X-21=0

a = 1; b = 2; c = -21;
Δ = b2-4ac
Δ = 22-4·1·(-21)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{22}}{2*1}=\frac{-2-2\sqrt{22}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{22}}{2*1}=\frac{-2+2\sqrt{22}}{2}
$