5/2x+1/2x=5+72x

Solution for 5/2x+1/2x=5+72x equation:

5/2x+1/2x=5+72x

We move all terms to the left:

5/2x+1/2x-(5+72x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

5/2x+1/2x-(72x+5)=0

We get rid of parentheses

5/2x+1/2x-72x-5=0

We multiply all the terms by the denominator


-72x*2x-5*2x+5+1=0

We add all the numbers together, and all the variables

-72x*2x-5*2x+6=0

Wy multiply elements

-144x^2-10x+6=0

a = -144; b = -10; c = +6;
Δ = b2-4ac
Δ = -102-4·(-144)·6
Δ = 3556
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:

$\sqrt{\Delta}=\sqrt{3556}=\sqrt{4*889}=\sqrt{4}*\sqrt{889}=2\sqrt{889}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{889}}{2*-144}=\frac{10-2\sqrt{889}}{-288}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{889}}{2*-144}=\frac{10+2\sqrt{889}}{-288}
$