4/3x=3x-7

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

4/3x=3x-7

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

4/3x-3x+7=0

We multiply all the terms by the denominator


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

Wy multiply elements

-9x^2+21x+4=0

a = -9; b = 21; c = +4;
Δ = b2-4ac
Δ = 212-4·(-9)·4
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{65}}{2*-9}=\frac{-21-3\sqrt{65}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{65}}{2*-9}=\frac{-21+3\sqrt{65}}{-18}
$