7/(x-9)=4x

Solution for 7/(x-9)=4x equation:

7/(x-9)=4x

We move all terms to the left:

7/(x-9)-(4x)=0


Domain of the equation: (x-9)!=0

We move all terms containing x to the left, all other terms to the right

x!=9

x∈R


We add all the numbers together, and all the variables

-4x+7/(x-9)=0

We multiply all the terms by the denominator


-4x*(x-9)+7=0

We multiply parentheses

-4x^2+36x+7=0

a = -4; b = 36; c = +7;
Δ = b2-4ac
Δ = 362-4·(-4)·7
Δ = 1408
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:

$\sqrt{\Delta}=\sqrt{1408}=\sqrt{64*22}=\sqrt{64}*\sqrt{22}=8\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-8\sqrt{22}}{2*-4}=\frac{-36-8\sqrt{22}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+8\sqrt{22}}{2*-4}=\frac{-36+8\sqrt{22}}{-8}
$