5x+1/2x=22+7/2x

Solution for 5x+1/2x=22+7/2x equation:

5x+1/2x=22+7/2x

We move all terms to the left:

5x+1/2x-(22+7/2x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x+1/2x-(7/2x+22)=0

We get rid of parentheses

5x+1/2x-7/2x-22=0

We multiply all the terms by the denominator


5x*2x-22*2x+1-7=0

We add all the numbers together, and all the variables

5x*2x-22*2x-6=0

Wy multiply elements

10x^2-44x-6=0

a = 10; b = -44; c = -6;
Δ = b2-4ac
Δ = -442-4·10·(-6)
Δ = 2176
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:

$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-8\sqrt{34}}{2*10}=\frac{44-8\sqrt{34}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+8\sqrt{34}}{2*10}=\frac{44+8\sqrt{34}}{20}
$