5+3x=7/3(x)

Solution for 5+3x=7/3(x) equation:

5+3x=7/3(x)

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3x-7/3x+5=0

We multiply all the terms by the denominator


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

Wy multiply elements

9x^2+15x-7=0

a = 9; b = 15; c = -7;
Δ = b2-4ac
Δ = 152-4·9·(-7)
Δ = 477
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:

$\sqrt{\Delta}=\sqrt{477}=\sqrt{9*53}=\sqrt{9}*\sqrt{53}=3\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{53}}{2*9}=\frac{-15-3\sqrt{53}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{53}}{2*9}=\frac{-15+3\sqrt{53}}{18}
$