7x=24/x+13

Solution for 7x=24/x+13 equation:

7x=24/x+13

We move all terms to the left:

7x-(24/x+13)=0


Domain of the equation: x+13)!=0

x∈R


We get rid of parentheses

7x-24/x-13=0

We multiply all the terms by the denominator


7x*x-13*x-24=0

We add all the numbers together, and all the variables

-13x+7x*x-24=0

Wy multiply elements

7x^2-13x-24=0

a = 7; b = -13; c = -24;
Δ = b2-4ac
Δ = -132-4·7·(-24)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-29}{2*7}=\frac{-16}{14}
=-1+1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+29}{2*7}=\frac{42}{14}
=3
$