2-3x=3/7x+6

Solution for 2-3x=3/7x+6 equation:

2-3x=3/7x+6

We move all terms to the left:

2-3x-(3/7x+6)=0


Domain of the equation: 7x+6)!=0

x∈R


We get rid of parentheses

-3x-3/7x-6+2=0

We multiply all the terms by the denominator


-3x*7x-6*7x+2*7x-3=0

Wy multiply elements

-21x^2-42x+14x-3=0

We add all the numbers together, and all the variables

-21x^2-28x-3=0

a = -21; b = -28; c = -3;
Δ = b2-4ac
Δ = -282-4·(-21)·(-3)
Δ = 532
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:

$\sqrt{\Delta}=\sqrt{532}=\sqrt{4*133}=\sqrt{4}*\sqrt{133}=2\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{133}}{2*-21}=\frac{28-2\sqrt{133}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{133}}{2*-21}=\frac{28+2\sqrt{133}}{-42}
$