(3/3x-7)=4x-8

Solution for (3/3x-7)=4x-8 equation:

(3/3x-7)=4x-8

We move all terms to the left:

(3/3x-7)-(4x-8)=0


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

x∈R


We get rid of parentheses

3/3x-4x-7+8=0

We multiply all the terms by the denominator


-4x*3x-7*3x+8*3x+3=0

Wy multiply elements

-12x^2-21x+24x+3=0

We add all the numbers together, and all the variables

-12x^2+3x+3=0

a = -12; b = 3; c = +3;
Δ = b2-4ac
Δ = 32-4·(-12)·3
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{17}}{2*-12}=\frac{-3-3\sqrt{17}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{17}}{2*-12}=\frac{-3+3\sqrt{17}}{-24}
$