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

Solution for (-12)(x)=2/3x+7 equation:

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

We move all terms to the left:

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


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

x∈R


We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -36; b = -21; c = -2;
Δ = b2-4ac
Δ = -212-4·(-36)·(-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{-(-21)-3\sqrt{17}}{2*-36}=\frac{21-3\sqrt{17}}{-72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{17}}{2*-36}=\frac{21+3\sqrt{17}}{-72}
$