(x-5)(7-x)=0

Solution for (x-5)(7-x)=0 equation:

(x-5)(7-x)=0

We add all the numbers together, and all the variables

(x-5)(-1x+7)=0

We multiply parentheses ..

(-1x^2+7x+5x-35)=0

We get rid of parentheses

-1x^2+7x+5x-35=0

We add all the numbers together, and all the variables

-1x^2+12x-35=0

a = -1; b = 12; c = -35;
Δ = b2-4ac
Δ = 122-4·(-1)·(-35)
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{-(12)-2}{2*-1}=\frac{-14}{-2}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2}{2*-1}=\frac{-10}{-2}
=+5
$