/7x-3=21-x

Solution for /7x-3=21-x equation:

/7x-3=21-x

We move all terms to the left:

/7x-3-(21-x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

/7x-(-1x+21)-3=0

We get rid of parentheses

/7x+1x-21-3=0

We multiply all the terms by the denominator


1x*7x-21*7x-3*7x+=0

We add all the numbers together, and all the variables

1x*7x-21*7x-3*7x=0

Wy multiply elements

7x^2-147x-21x=0

We add all the numbers together, and all the variables

7x^2-168x=0

a = 7; b = -168; c = 0;
Δ = b2-4ac
Δ = -1682-4·7·0
Δ = 28224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28224}=168$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-168)-168}{2*7}=\frac{0}{14}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-168)+168}{2*7}=\frac{336}{14}
=24
$