(x-8)(5-x)=-2

Solution for (x-8)(5-x)=-2 equation:

(x-8)(5-x)=-2

We move all terms to the left:

(x-8)(5-x)-(-2)=0

We add all the numbers together, and all the variables

(x-8)(-1x+5)-(-2)=0

We add all the numbers together, and all the variables

(x-8)(-1x+5)+2=0

We multiply parentheses ..

(-1x^2+5x+8x-40)+2=0

We get rid of parentheses

-1x^2+5x+8x-40+2=0

We add all the numbers together, and all the variables

-1x^2+13x-38=0

a = -1; b = 13; c = -38;
Δ = b2-4ac
Δ = 132-4·(-1)·(-38)
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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