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

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

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

We move all terms to the left:

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


Domain of the equation: 33x!=0

x!=0/33

x!=0

x∈R


We get rid of parentheses

2/33x-2x+7=0

We multiply all the terms by the denominator


-2x*33x+7*33x+2=0

Wy multiply elements

-66x^2+231x+2=0

a = -66; b = 231; c = +2;
Δ = b2-4ac
Δ = 2312-4·(-66)·2
Δ = 53889
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{-(231)-\sqrt{53889}}{2*-66}=\frac{-231-\sqrt{53889}}{-132}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(231)+\sqrt{53889}}{2*-66}=\frac{-231+\sqrt{53889}}{-132}
$