3/4x-9=4(x1)

Solution for 3/4x-9=4(x1) equation:

3/4x-9=4(x1)

We move all terms to the left:

3/4x-9-(4(x1))=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


determiningTheFunctionDomain
3/4x-4x1-9=0

We add all the numbers together, and all the variables

-4x+3/4x-9=0

We multiply all the terms by the denominator


-4x*4x-9*4x+3=0

Wy multiply elements

-16x^2-36x+3=0

a = -16; b = -36; c = +3;
Δ = b2-4ac
Δ = -362-4·(-16)·3
Δ = 1488
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:

$\sqrt{\Delta}=\sqrt{1488}=\sqrt{16*93}=\sqrt{16}*\sqrt{93}=4\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{93}}{2*-16}=\frac{36-4\sqrt{93}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{93}}{2*-16}=\frac{36+4\sqrt{93}}{-32}
$