-78=-19x+x^2

Solution for -78=-19x+x^2 equation:

-78=-19x+x^2

We move all terms to the left:

-78-(-19x+x^2)=0

We get rid of parentheses

-x^2+19x-78=0

We add all the numbers together, and all the variables

-1x^2+19x-78=0

a = -1; b = 19; c = -78;
Δ = b2-4ac
Δ = 192-4·(-1)·(-78)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-7}{2*-1}=\frac{-26}{-2}
=+13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+7}{2*-1}=\frac{-12}{-2}
=+6
$