2x+6=2/35x-9

Solution for 2x+6=2/35x-9 equation:

2x+6=2/35x-9

We move all terms to the left:

2x+6-(2/35x-9)=0


Domain of the equation: 35x-9)!=0

x∈R


We get rid of parentheses

2x-2/35x+9+6=0

We multiply all the terms by the denominator


2x*35x+9*35x+6*35x-2=0

Wy multiply elements

70x^2+315x+210x-2=0

We add all the numbers together, and all the variables

70x^2+525x-2=0

a = 70; b = 525; c = -2;
Δ = b2-4ac
Δ = 5252-4·70·(-2)
Δ = 276185
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{-(525)-\sqrt{276185}}{2*70}=\frac{-525-\sqrt{276185}}{140}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(525)+\sqrt{276185}}{2*70}=\frac{-525+\sqrt{276185}}{140}
$