a(68-a)=256

Solution for a(68-a)=256 equation:

a(68-a)=256

We move all terms to the left:

a(68-a)-(256)=0

We add all the numbers together, and all the variables

a(-1a+68)-256=0

We multiply parentheses

-1a^2+68a-256=0

a = -1; b = 68; c = -256;
Δ = b2-4ac
Δ = 682-4·(-1)·(-256)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-60}{2*-1}=\frac{-128}{-2}
=+64
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+60}{2*-1}=\frac{-8}{-2}
=+4
$