X(x-1)-10x+35=5

Solution for X(x-1)-10x+35=5 equation:

X(X-1)-10X+35=5

We move all terms to the left:

X(X-1)-10X+35-(5)=0

We add all the numbers together, and all the variables

-10X+X(X-1)+30=0

We multiply parentheses

X^2-10X-1X+30=0

We add all the numbers together, and all the variables

X^2-11X+30=0

a = 1; b = -11; c = +30;
Δ = b2-4ac
Δ = -112-4·1·30
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-1}{2*1}=\frac{10}{2}
=5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+1}{2*1}=\frac{12}{2}
=6
$