(x-6)*(10-x)=0

Solution for (x-6)*(10-x)=0 equation:

(x-6)(10-x)=0

We add all the numbers together, and all the variables

(x-6)(-1x+10)=0

We multiply parentheses ..

(-1x^2+10x+6x-60)=0

We get rid of parentheses

-1x^2+10x+6x-60=0

We add all the numbers together, and all the variables

-1x^2+16x-60=0

a = -1; b = 16; c = -60;
Δ = b2-4ac
Δ = 162-4·(-1)·(-60)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4}{2*-1}=\frac{-20}{-2}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4}{2*-1}=\frac{-12}{-2}
=+6
$