5a-180/a=-25

Solution for 5a-180/a=-25 equation:

5a-180/a=-25

We move all terms to the left:

5a-180/a-(-25)=0


Domain of the equation: a!=0

a∈R


We add all the numbers together, and all the variables

5a-180/a+25=0

We multiply all the terms by the denominator


5a*a+25*a-180=0

We add all the numbers together, and all the variables

25a+5a*a-180=0

Wy multiply elements

5a^2+25a-180=0

a = 5; b = 25; c = -180;
Δ = b2-4ac
Δ = 252-4·5·(-180)
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-65}{2*5}=\frac{-90}{10}
=-9
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+65}{2*5}=\frac{40}{10}
=4
$