9/4x(4-3)=9x+11

Solution for 9/4x(4-3)=9x+11 equation:

9/4x(4-3)=9x+11

We move all terms to the left:

9/4x(4-3)-(9x+11)=0


Domain of the equation: 4x(4-3)!=0

x∈R


We add all the numbers together, and all the variables

9/4x1-(9x+11)=0

We get rid of parentheses

9/4x1-9x-11=0

We multiply all the terms by the denominator


-9x*4x1-11*4x1+9=0

Wy multiply elements

-36x^2-44x+9=0

a = -36; b = -44; c = +9;
Δ = b2-4ac
Δ = -442-4·(-36)·9
Δ = 3232
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:

$\sqrt{\Delta}=\sqrt{3232}=\sqrt{16*202}=\sqrt{16}*\sqrt{202}=4\sqrt{202}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{202}}{2*-36}=\frac{44-4\sqrt{202}}{-72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{202}}{2*-36}=\frac{44+4\sqrt{202}}{-72}
$