x=-4x-7/x-12

Solution for x=-4x-7/x-12 equation:

x=-4x-7/x-12

We move all terms to the left:

x-(-4x-7/x-12)=0


Domain of the equation: x-12)!=0

x∈R


We get rid of parentheses

x+4x+7/x+12=0

We multiply all the terms by the denominator


x*x+4x*x+12*x+7=0

We add all the numbers together, and all the variables

12x+x*x+4x*x+7=0

Wy multiply elements

x^2+4x^2+12x+7=0

We add all the numbers together, and all the variables

5x^2+12x+7=0

a = 5; b = 12; c = +7;
Δ = b2-4ac
Δ = 122-4·5·7
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2}{2*5}=\frac{-14}{10}
=-1+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2}{2*5}=\frac{-10}{10}
=-1
$