7x=32+5/3x

Solution for 7x=32+5/3x equation:

7x=32+5/3x

We move all terms to the left:

7x-(32+5/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7x-(5/3x+32)=0

We get rid of parentheses

7x-5/3x-32=0

We multiply all the terms by the denominator


7x*3x-32*3x-5=0

Wy multiply elements

21x^2-96x-5=0

a = 21; b = -96; c = -5;
Δ = b2-4ac
Δ = -962-4·21·(-5)
Δ = 9636
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:

$\sqrt{\Delta}=\sqrt{9636}=\sqrt{4*2409}=\sqrt{4}*\sqrt{2409}=2\sqrt{2409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-2\sqrt{2409}}{2*21}=\frac{96-2\sqrt{2409}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+2\sqrt{2409}}{2*21}=\frac{96+2\sqrt{2409}}{42}
$