(-12x^2-9x)/x=-4x-3

Solution for (-12x^2-9x)/x=-4x-3 equation:

(-12x^2-9x)/x=-4x-3

We move all terms to the left:

(-12x^2-9x)/x-(-4x-3)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

(-12x^2-9x)/x+4x+3=0

We multiply all the terms by the denominator


(-12x^2-9x)+4x*x+3*x=0

We add all the numbers together, and all the variables

(-12x^2-9x)+3x+4x*x=0

Wy multiply elements

(-12x^2-9x)+4x^2+3x=0

We get rid of parentheses

-12x^2+4x^2-9x+3x=0

We add all the numbers together, and all the variables

-8x^2-6x=0

a = -8; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-8)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-8}=\frac{0}{-16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-8}=\frac{12}{-16}
=-3/4
$