(x-8)(7-x)=0

Solution for (x-8)(7-x)=0 equation:

(x-8)(7-x)=0

We add all the numbers together, and all the variables

(x-8)(-1x+7)=0

We multiply parentheses ..

(-1x^2+7x+8x-56)=0

We get rid of parentheses

-1x^2+7x+8x-56=0

We add all the numbers together, and all the variables

-1x^2+15x-56=0

a = -1; b = 15; c = -56;
Δ = b2-4ac
Δ = 152-4·(-1)·(-56)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-1}{2*-1}=\frac{-16}{-2}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+1}{2*-1}=\frac{-14}{-2}
=+7
$