7(x-5)(3-x)=0

Solution for 7(x-5)(3-x)=0 equation:

7(x-5)(3-x)=0

We add all the numbers together, and all the variables

7(x-5)(-1x+3)=0

We multiply parentheses ..

7(-1x^2+3x+5x-15)=0

We multiply parentheses

-7x^2+21x+35x-105=0

We add all the numbers together, and all the variables

-7x^2+56x-105=0

a = -7; b = 56; c = -105;
Δ = b2-4ac
Δ = 562-4·(-7)·(-105)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-14}{2*-7}=\frac{-70}{-14}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+14}{2*-7}=\frac{-42}{-14}
=+3
$