5/3x=5x-19

Solution for 5/3x=5x-19 equation:

5/3x=5x-19

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

5/3x-5x+19=0

We multiply all the terms by the denominator


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

Wy multiply elements

-15x^2+57x+5=0

a = -15; b = 57; c = +5;
Δ = b2-4ac
Δ = 572-4·(-15)·5
Δ = 3549
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:

$\sqrt{\Delta}=\sqrt{3549}=\sqrt{169*21}=\sqrt{169}*\sqrt{21}=13\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-13\sqrt{21}}{2*-15}=\frac{-57-13\sqrt{21}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+13\sqrt{21}}{2*-15}=\frac{-57+13\sqrt{21}}{-30}
$