4/4+2x=11/24.5x

Solution for 4/4+2x=11/24.5x equation:

4/4+2x=11/24.5x

We move all terms to the left:

4/4+2x-(11/24.5x)=0


Domain of the equation: 24.5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+11/24.5x)+4/4=0

We add all the numbers together, and all the variables

2x-(+11/24.5x)+1=0

We get rid of parentheses

2x-11/24.5x+1=0

We multiply all the terms by the denominator


2x*24.5x+1*24.5x-11=0

Wy multiply elements

48x^2+24x-11=0

a = 48; b = 24; c = -11;
Δ = b2-4ac
Δ = 242-4·48·(-11)
Δ = 2688
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:

$\sqrt{\Delta}=\sqrt{2688}=\sqrt{64*42}=\sqrt{64}*\sqrt{42}=8\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{42}}{2*48}=\frac{-24-8\sqrt{42}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{42}}{2*48}=\frac{-24+8\sqrt{42}}{96}
$