2/3x+4=2+17x

Solution for 2/3x+4=2+17x equation:

2/3x+4=2+17x

We move all terms to the left:

2/3x+4-(2+17x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(17x+2)+4=0

We get rid of parentheses

2/3x-17x-2+4=0

We multiply all the terms by the denominator


-17x*3x-2*3x+4*3x+2=0

Wy multiply elements

-51x^2-6x+12x+2=0

We add all the numbers together, and all the variables

-51x^2+6x+2=0

a = -51; b = 6; c = +2;
Δ = b2-4ac
Δ = 62-4·(-51)·2
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{111}}{2*-51}=\frac{-6-2\sqrt{111}}{-102}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{111}}{2*-51}=\frac{-6+2\sqrt{111}}{-102}
$