-3x=2/3x-7

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

-3x=2/3x-7

We move all terms to the left:

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


Domain of the equation: 3x-7)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-9x^2+21x-2=0

a = -9; b = 21; c = -2;
Δ = b2-4ac
Δ = 212-4·(-9)·(-2)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{41}}{2*-9}=\frac{-21-3\sqrt{41}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{41}}{2*-9}=\frac{-21+3\sqrt{41}}{-18}
$