x-7=19-2/3*x

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

x-7=19-2/3x

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2-57x-21x+2=0

We add all the numbers together, and all the variables

3x^2-78x+2=0

a = 3; b = -78; c = +2;
Δ = b2-4ac
Δ = -782-4·3·2
Δ = 6060
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:

$\sqrt{\Delta}=\sqrt{6060}=\sqrt{4*1515}=\sqrt{4}*\sqrt{1515}=2\sqrt{1515}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{1515}}{2*3}=\frac{78-2\sqrt{1515}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{1515}}{2*3}=\frac{78+2\sqrt{1515}}{6}
$