36/4x+9=-2+8x

Solution for 36/4x+9=-2+8x equation:

36/4x+9=-2+8x

We move all terms to the left:

36/4x+9-(-2+8x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

36/4x-(8x-2)+9=0

We get rid of parentheses

36/4x-8x+2+9=0

We multiply all the terms by the denominator


-8x*4x+2*4x+9*4x+36=0

Wy multiply elements

-32x^2+8x+36x+36=0

We add all the numbers together, and all the variables

-32x^2+44x+36=0

a = -32; b = 44; c = +36;
Δ = b2-4ac
Δ = 442-4·(-32)·36
Δ = 6544
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:

$\sqrt{\Delta}=\sqrt{6544}=\sqrt{16*409}=\sqrt{16}*\sqrt{409}=4\sqrt{409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{409}}{2*-32}=\frac{-44-4\sqrt{409}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{409}}{2*-32}=\frac{-44+4\sqrt{409}}{-64}
$