5x+7=19/3x

Solution for 5x+7=19/3x equation:

5x+7=19/3x

We move all terms to the left:

5x+7-(19/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(+19/3x)+7=0

We get rid of parentheses

5x-19/3x+7=0

We multiply all the terms by the denominator


5x*3x+7*3x-19=0

Wy multiply elements

15x^2+21x-19=0

a = 15; b = 21; c = -19;
Δ = b2-4ac
Δ = 212-4·15·(-19)
Δ = 1581
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{-(21)-\sqrt{1581}}{2*15}=\frac{-21-\sqrt{1581}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{1581}}{2*15}=\frac{-21+\sqrt{1581}}{30}
$