a^2+.25=a+4

Solution for a^2+.25=a+4 equation:

a^2+.25=a+4

We move all terms to the left:

a^2+.25-(a+4)=0

We add all the numbers together, and all the variables

a^2-(a+4)+0.25=0

We get rid of parentheses

a^2-a-4+0.25=0

We add all the numbers together, and all the variables

a^2-1a-3.75=0

a = 1; b = -1; c = -3.75;
Δ = b2-4ac
Δ = -12-4·1·(-3.75)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-4}{2*1}=\frac{-3}{2}
=-1+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+4}{2*1}=\frac{5}{2}
=2+1/2
$