14/3x+16=21-x

Solution for 14/3x+16=21-x equation:

14/3x+16=21-x

We move all terms to the left:

14/3x+16-(21-x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

14/3x-(-1x+21)+16=0

We get rid of parentheses

14/3x+1x-21+16=0

We multiply all the terms by the denominator


1x*3x-21*3x+16*3x+14=0

Wy multiply elements

3x^2-63x+48x+14=0

We add all the numbers together, and all the variables

3x^2-15x+14=0

a = 3; b = -15; c = +14;
Δ = b2-4ac
Δ = -152-4·3·14
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{57}}{2*3}=\frac{15-\sqrt{57}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{57}}{2*3}=\frac{15+\sqrt{57}}{6}
$