5/2a+5=25a=

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

5/2a+5=25a=

We move all terms to the left:

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


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-50a^2+10a+5=0

a = -50; b = 10; c = +5;
Δ = b2-4ac
Δ = 102-4·(-50)·5
Δ = 1100
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:

$\sqrt{\Delta}=\sqrt{1100}=\sqrt{100*11}=\sqrt{100}*\sqrt{11}=10\sqrt{11}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{11}}{2*-50}=\frac{-10-10\sqrt{11}}{-100}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{11}}{2*-50}=\frac{-10+10\sqrt{11}}{-100}
$