2/3x+19=35x

Solution for 2/3x+19=35x equation:

2/3x+19=35x

We move all terms to the left:

2/3x+19-(35x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-35x+2/3x+19=0

We multiply all the terms by the denominator


-35x*3x+19*3x+2=0

Wy multiply elements

-105x^2+57x+2=0

a = -105; b = 57; c = +2;
Δ = b2-4ac
Δ = 572-4·(-105)·2
Δ = 4089
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{-(57)-\sqrt{4089}}{2*-105}=\frac{-57-\sqrt{4089}}{-210}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+\sqrt{4089}}{2*-105}=\frac{-57+\sqrt{4089}}{-210}
$