7/x-4x+6=18

Solution for 7/x-4x+6=18 equation:

7/x-4x+6=18

We move all terms to the left:

7/x-4x+6-(18)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-4x+7/x-12=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -4; b = -12; c = +7;
Δ = b2-4ac
Δ = -122-4·(-4)·7
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-16}{2*-4}=\frac{-4}{-8}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+16}{2*-4}=\frac{28}{-8}
=-3+1/2
$