4/3x+7=2x-9

Solution for 4/3x+7=2x-9 equation:

4/3x+7=2x-9

We move all terms to the left:

4/3x+7-(2x-9)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

4/3x-2x+9+7=0

We multiply all the terms by the denominator


-2x*3x+9*3x+7*3x+4=0

Wy multiply elements

-6x^2+27x+21x+4=0

We add all the numbers together, and all the variables

-6x^2+48x+4=0

a = -6; b = 48; c = +4;
Δ = b2-4ac
Δ = 482-4·(-6)·4
Δ = 2400
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:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-20\sqrt{6}}{2*-6}=\frac{-48-20\sqrt{6}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+20\sqrt{6}}{2*-6}=\frac{-48+20\sqrt{6}}{-12}
$