X=78x-x^2

Solution for X=78x-x^2 equation:

X=78X-X^2

We move all terms to the left:

X-(78X-X^2)=0

We get rid of parentheses

X^2-78X+X=0

We add all the numbers together, and all the variables

X^2-77X=0

a = 1; b = -77; c = 0;
Δ = b2-4ac
Δ = -772-4·1·0
Δ = 5929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5929}=77$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-77)-77}{2*1}=\frac{0}{2}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+77}{2*1}=\frac{154}{2}
=77
$