21x-x^2=68

Solution for 21x-x^2=68 equation:

21x-x^2=68

We move all terms to the left:

21x-x^2-(68)=0

We add all the numbers together, and all the variables

-1x^2+21x-68=0

a = -1; b = 21; c = -68;
Δ = b2-4ac
Δ = 212-4·(-1)·(-68)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-13}{2*-1}=\frac{-34}{-2}
=+17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+13}{2*-1}=\frac{-8}{-2}
=+4
$