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

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

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

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

6x^2+48x+2=0

a = 6; b = 48; c = +2;
Δ = b2-4ac
Δ = 482-4·6·2
Δ = 2256
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:

$\sqrt{\Delta}=\sqrt{2256}=\sqrt{16*141}=\sqrt{16}*\sqrt{141}=4\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{141}}{2*6}=\frac{-48-4\sqrt{141}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{141}}{2*6}=\frac{-48+4\sqrt{141}}{12}
$