38a=28-a^2

Solution for 38a=28-a^2 equation:

38a=28-a^2

We move all terms to the left:

38a-(28-a^2)=0

We get rid of parentheses

a^2+38a-28=0

a = 1; b = 38; c = -28;
Δ = b2-4ac
Δ = 382-4·1·(-28)
Δ = 1556
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:

$\sqrt{\Delta}=\sqrt{1556}=\sqrt{4*389}=\sqrt{4}*\sqrt{389}=2\sqrt{389}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-2\sqrt{389}}{2*1}=\frac{-38-2\sqrt{389}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+2\sqrt{389}}{2*1}=\frac{-38+2\sqrt{389}}{2}
$