(x-4)(10-x)=8

Solution for (x-4)(10-x)=8 equation:

(x-4)(10-x)=8

We move all terms to the left:

(x-4)(10-x)-(8)=0

We add all the numbers together, and all the variables

(x-4)(-1x+10)-8=0

We multiply parentheses ..

(-1x^2+10x+4x-40)-8=0

We get rid of parentheses

-1x^2+10x+4x-40-8=0

We add all the numbers together, and all the variables

-1x^2+14x-48=0

a = -1; b = 14; c = -48;
Δ = b2-4ac
Δ = 142-4·(-1)·(-48)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2}{2*-1}=\frac{-16}{-2}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2}{2*-1}=\frac{-12}{-2}
=+6
$