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

Solution for (x-4)(10-x)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+14x-40=0

a = -1; b = 14; c = -40;
Δ = b2-4ac
Δ = 142-4·(-1)·(-40)
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{-(14)-6}{2*-1}=\frac{-20}{-2}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+6}{2*-1}=\frac{-8}{-2}
=+4
$