(32-x)x=247

Solution for (32-x)x=247 equation:

(32-x)x=247

We move all terms to the left:

(32-x)x-(247)=0

We add all the numbers together, and all the variables

(-1x+32)x-247=0

We multiply parentheses

-1x^2+32x-247=0

a = -1; b = 32; c = -247;
Δ = b2-4ac
Δ = 322-4·(-1)·(-247)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-6}{2*-1}=\frac{-38}{-2}
=+19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+6}{2*-1}=\frac{-26}{-2}
=+13
$