(3x-6)(x-5)-(5x-10)=5

Solution for (3x-6)(x-5)-(5x-10)=5 equation:

(3x-6)(x-5)-(5x-10)=5

We move all terms to the left:

(3x-6)(x-5)-(5x-10)-(5)=0

We get rid of parentheses

(3x-6)(x-5)-5x+10-5=0

We multiply parentheses ..

(+3x^2-15x-6x+30)-5x+10-5=0

We add all the numbers together, and all the variables

(+3x^2-15x-6x+30)-5x+5=0

We get rid of parentheses

3x^2-15x-6x-5x+30+5=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{10}{6}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+16}{2*3}=\frac{42}{6}
=7
$