3(x-4)=-2/3x-7

Solution for 3(x-4)=-2/3x-7 equation:

3(x-4)=-2/3x-7

We move all terms to the left:

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


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

x∈R


We multiply parentheses

3x-(-2/3x-7)-12=0

We get rid of parentheses

3x+2/3x+7-12=0

We multiply all the terms by the denominator


3x*3x+7*3x-12*3x+2=0

Wy multiply elements

9x^2+21x-36x+2=0

We add all the numbers together, and all the variables

9x^2-15x+2=0

a = 9; b = -15; c = +2;
Δ = b2-4ac
Δ = -152-4·9·2
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{-(-15)-3\sqrt{17}}{2*9}=\frac{15-3\sqrt{17}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{17}}{2*9}=\frac{15+3\sqrt{17}}{18}
$