(39-x)(x)=248

Solution for (39-x)(x)=248 equation:

(39-x)(x)=248

We move all terms to the left:

(39-x)(x)-(248)=0

We add all the numbers together, and all the variables

(-1x+39)x-248=0

We multiply parentheses

-1x^2+39x-248=0

a = -1; b = 39; c = -248;
Δ = b2-4ac
Δ = 392-4·(-1)·(-248)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-23}{2*-1}=\frac{-62}{-2}
=+31
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+23}{2*-1}=\frac{-16}{-2}
=+8
$