11/2x-9=5+4x

Solution for 11/2x-9=5+4x equation:

11/2x-9=5+4x

We move all terms to the left:

11/2x-9-(5+4x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

11/2x-(4x+5)-9=0

We get rid of parentheses

11/2x-4x-5-9=0

We multiply all the terms by the denominator


-4x*2x-5*2x-9*2x+11=0

Wy multiply elements

-8x^2-10x-18x+11=0

We add all the numbers together, and all the variables

-8x^2-28x+11=0

a = -8; b = -28; c = +11;
Δ = b2-4ac
Δ = -282-4·(-8)·11
Δ = 1136
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:

$\sqrt{\Delta}=\sqrt{1136}=\sqrt{16*71}=\sqrt{16}*\sqrt{71}=4\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{71}}{2*-8}=\frac{28-4\sqrt{71}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{71}}{2*-8}=\frac{28+4\sqrt{71}}{-16}
$