a+(1/4)a=31

Solution for a+(1/4)a=31 equation:

a+(1/4)a=31

We move all terms to the left:

a+(1/4)a-(31)=0


Domain of the equation: 4)a!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

a+(+1/4)a-31=0

We multiply parentheses

a^2+a-31=0

a = 1; b = 1; c = -31;
Δ = b2-4ac
Δ = 12-4·1·(-31)
Δ = 125
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:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5\sqrt{5}}{2*1}=\frac{-1-5\sqrt{5}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5\sqrt{5}}{2*1}=\frac{-1+5\sqrt{5}}{2}
$