7x-19=2/3x-19

Solution for 7x-19=2/3x-19 equation:

7x-19=2/3x-19

We move all terms to the left:

7x-19-(2/3x-19)=0


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

x∈R


We get rid of parentheses

7x-2/3x+19-19=0

We multiply all the terms by the denominator


7x*3x+19*3x-19*3x-2=0

Wy multiply elements

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

We add all the numbers together, and all the variables

21x^2-2=0

a = 21; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·21·(-2)
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{42}}{2*21}=\frac{0-2\sqrt{42}}{42}
=-\frac{2\sqrt{42}}{42}
=-\frac{\sqrt{42}}{21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{42}}{2*21}=\frac{0+2\sqrt{42}}{42}
=\frac{2\sqrt{42}}{42}
=\frac{\sqrt{42}}{21}
$