6/7x=2x-3

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

6/7x=2x-3

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

6/7x-2x+3=0

We multiply all the terms by the denominator


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

Wy multiply elements

-14x^2+21x+6=0

a = -14; b = 21; c = +6;
Δ = b2-4ac
Δ = 212-4·(-14)·6
Δ = 777
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{-(21)-\sqrt{777}}{2*-14}=\frac{-21-\sqrt{777}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{777}}{2*-14}=\frac{-21+\sqrt{777}}{-28}
$