19-7x=8-2/3x

Solution for 19-7x=8-2/3x equation:

19-7x=8-2/3x

We move all terms to the left:

19-7x-(8-2/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-7x-(-2/3x+8)+19=0

We get rid of parentheses

-7x+2/3x-8+19=0

We multiply all the terms by the denominator


-7x*3x-8*3x+19*3x+2=0

Wy multiply elements

-21x^2-24x+57x+2=0

We add all the numbers together, and all the variables

-21x^2+33x+2=0

a = -21; b = 33; c = +2;
Δ = b2-4ac
Δ = 332-4·(-21)·2
Δ = 1257
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{-(33)-\sqrt{1257}}{2*-21}=\frac{-33-\sqrt{1257}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{1257}}{2*-21}=\frac{-33+\sqrt{1257}}{-42}
$