273-8x-x^2=0

Solution for 273-8x-x^2=0 equation:

273-8x-x^2=0

We add all the numbers together, and all the variables

-1x^2-8x+273=0

a = -1; b = -8; c = +273;
Δ = b2-4ac
Δ = -82-4·(-1)·273
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-34}{2*-1}=\frac{-26}{-2}
=+13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+34}{2*-1}=\frac{42}{-2}
=-21
$