5a-15=5/4a

Solution for 5a-15=5/4a equation:

5a-15=5/4a

We move all terms to the left:

5a-15-(5/4a)=0


Domain of the equation: 4a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

5a-(+5/4a)-15=0

We get rid of parentheses

5a-5/4a-15=0

We multiply all the terms by the denominator


5a*4a-15*4a-5=0

Wy multiply elements

20a^2-60a-5=0

a = 20; b = -60; c = -5;
Δ = b2-4ac
Δ = -602-4·20·(-5)
Δ = 4000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4000}=\sqrt{400*10}=\sqrt{400}*\sqrt{10}=20\sqrt{10}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-20\sqrt{10}}{2*20}=\frac{60-20\sqrt{10}}{40}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+20\sqrt{10}}{2*20}=\frac{60+20\sqrt{10}}{40}
$