7x+5=5/3x-19=9

Solution for 7x+5=5/3x-19=9 equation:

7x+5=5/3x-19=9

We move all terms to the left:

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


Domain of the equation: 3x-19)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

21x^2+57x+15x-5=0

We add all the numbers together, and all the variables

21x^2+72x-5=0

a = 21; b = 72; c = -5;
Δ = b2-4ac
Δ = 722-4·21·(-5)
Δ = 5604
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:

$\sqrt{\Delta}=\sqrt{5604}=\sqrt{4*1401}=\sqrt{4}*\sqrt{1401}=2\sqrt{1401}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-2\sqrt{1401}}{2*21}=\frac{-72-2\sqrt{1401}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+2\sqrt{1401}}{2*21}=\frac{-72+2\sqrt{1401}}{42}
$