(3-x)(x-7)=0

Solution for (3-x)(x-7)=0 equation:

(3-x)(x-7)=0

We add all the numbers together, and all the variables

(-1x+3)(x-7)=0

We multiply parentheses ..

(-1x^2+7x+3x-21)=0

We get rid of parentheses

-1x^2+7x+3x-21=0

We add all the numbers together, and all the variables

-1x^2+10x-21=0

a = -1; b = 10; c = -21;
Δ = b2-4ac
Δ = 102-4·(-1)·(-21)
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{-(10)-4}{2*-1}=\frac{-14}{-2}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4}{2*-1}=\frac{-6}{-2}
=+3
$