(x-8)(42-x)=2x-16

Solution for (x-8)(42-x)=2x-16 equation:

(x-8)(42-x)=2x-16

We move all terms to the left:

(x-8)(42-x)-(2x-16)=0

We add all the numbers together, and all the variables

(x-8)(-1x+42)-(2x-16)=0

We get rid of parentheses

(x-8)(-1x+42)-2x+16=0

We multiply parentheses ..

(-1x^2+42x+8x-336)-2x+16=0

We get rid of parentheses

-1x^2+42x+8x-2x-336+16=0

We add all the numbers together, and all the variables

-1x^2+48x-320=0

a = -1; b = 48; c = -320;
Δ = b2-4ac
Δ = 482-4·(-1)·(-320)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-32}{2*-1}=\frac{-80}{-2}
=+40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+32}{2*-1}=\frac{-16}{-2}
=+8
$