2/3x-3=4x-7

Solution for 2/3x-3=4x-7 equation:

2/3x-3=4x-7

We move all terms to the left:

2/3x-3-(4x-7)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-4x+7-3=0

We multiply all the terms by the denominator


-4x*3x+7*3x-3*3x+2=0

Wy multiply elements

-12x^2+21x-9x+2=0

We add all the numbers together, and all the variables

-12x^2+12x+2=0

a = -12; b = 12; c = +2;
Δ = b2-4ac
Δ = 122-4·(-12)·2
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{15}}{2*-12}=\frac{-12-4\sqrt{15}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{15}}{2*-12}=\frac{-12+4\sqrt{15}}{-24}
$