5x-19=4/3x+24

Solution for 5x-19=4/3x+24 equation:

5x-19=4/3x+24

We move all terms to the left:

5x-19-(4/3x+24)=0


Domain of the equation: 3x+24)!=0

x∈R


We get rid of parentheses

5x-4/3x-24-19=0

We multiply all the terms by the denominator


5x*3x-24*3x-19*3x-4=0

Wy multiply elements

15x^2-72x-57x-4=0

We add all the numbers together, and all the variables

15x^2-129x-4=0

a = 15; b = -129; c = -4;
Δ = b2-4ac
Δ = -1292-4·15·(-4)
Δ = 16881
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{-(-129)-\sqrt{16881}}{2*15}=\frac{129-\sqrt{16881}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-129)+\sqrt{16881}}{2*15}=\frac{129+\sqrt{16881}}{30}
$