2a-5=25/a

Solution for 2a-5=25/a equation:

2a-5=25/a

We move all terms to the left:

2a-5-(25/a)=0


Domain of the equation: a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

2a-(+25/a)-5=0

We get rid of parentheses

2a-25/a-5=0

We multiply all the terms by the denominator


2a*a-5*a-25=0

We add all the numbers together, and all the variables

-5a+2a*a-25=0

Wy multiply elements

2a^2-5a-25=0

a = 2; b = -5; c = -25;
Δ = b2-4ac
Δ = -52-4·2·(-25)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-15}{2*2}=\frac{-10}{4}
=-2+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+15}{2*2}=\frac{20}{4}
=5
$