2/3x=35x+-105

Solution for 2/3x=35x+-105 equation:

2/3x=35x+-105

We move all terms to the left:

2/3x-(35x+-105)=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-(35x-105)=0

We get rid of parentheses

2/3x-35x+105=0

We multiply all the terms by the denominator


-35x*3x+105*3x+2=0

Wy multiply elements

-105x^2+315x+2=0

a = -105; b = 315; c = +2;
Δ = b2-4ac
Δ = 3152-4·(-105)·2
Δ = 100065
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{-(315)-\sqrt{100065}}{2*-105}=\frac{-315-\sqrt{100065}}{-210}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(315)+\sqrt{100065}}{2*-105}=\frac{-315+\sqrt{100065}}{-210}
$