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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-3x^2+5x+21x-35)=0

We get rid of parentheses

-3x^2+5x+21x-35=0

We add all the numbers together, and all the variables

-3x^2+26x-35=0

a = -3; b = 26; c = -35;
Δ = b2-4ac
Δ = 262-4·(-3)·(-35)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-16}{2*-3}=\frac{-42}{-6}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+16}{2*-3}=\frac{-10}{-6}
=1+2/3
$