3x+6-9/4x=17

Solution for 3x+6-9/4x=17 equation:

3x+6-9/4x=17

We move all terms to the left:

3x+6-9/4x-(17)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3x-9/4x-11=0

We multiply all the terms by the denominator


3x*4x-11*4x-9=0

Wy multiply elements

12x^2-44x-9=0

a = 12; b = -44; c = -9;
Δ = b2-4ac
Δ = -442-4·12·(-9)
Δ = 2368
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:

$\sqrt{\Delta}=\sqrt{2368}=\sqrt{64*37}=\sqrt{64}*\sqrt{37}=8\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-8\sqrt{37}}{2*12}=\frac{44-8\sqrt{37}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+8\sqrt{37}}{2*12}=\frac{44+8\sqrt{37}}{24}
$