24/x=14-x

Solution for 24/x=14-x equation:

24/x=14-x

We move all terms to the left:

24/x-(14-x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

24/x-(-1x+14)=0

We get rid of parentheses

24/x+1x-14=0

We multiply all the terms by the denominator


1x*x-14*x+24=0

We add all the numbers together, and all the variables

-14x+1x*x+24=0

Wy multiply elements

x^2-14x+24=0

a = 1; b = -14; c = +24;
Δ = b2-4ac
Δ = -142-4·1·24
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-10}{2*1}=\frac{4}{2}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+10}{2*1}=\frac{24}{2}
=12
$