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

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

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

We move all terms to the left:

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


Domain of the equation: 3x+9)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

12x^2-27x-21x+2=0

We add all the numbers together, and all the variables

12x^2-48x+2=0

a = 12; b = -48; c = +2;
Δ = b2-4ac
Δ = -482-4·12·2
Δ = 2208
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:

$\sqrt{\Delta}=\sqrt{2208}=\sqrt{16*138}=\sqrt{16}*\sqrt{138}=4\sqrt{138}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{138}}{2*12}=\frac{48-4\sqrt{138}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{138}}{2*12}=\frac{48+4\sqrt{138}}{24}
$