(x-6)(x-1)=4x-18

Solution for (x-6)(x-1)=4x-18 equation:

(x-6)(x-1)=4x-18

We move all terms to the left:

(x-6)(x-1)-(4x-18)=0

We get rid of parentheses

(x-6)(x-1)-4x+18=0

We multiply parentheses ..

(+x^2-1x-6x+6)-4x+18=0

We get rid of parentheses

x^2-1x-6x-4x+6+18=0

We add all the numbers together, and all the variables

x^2-11x+24=0

a = 1; b = -11; c = +24;
Δ = b2-4ac
Δ = -112-4·1·24
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-5}{2*1}=\frac{6}{2}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+5}{2*1}=\frac{16}{2}
=8
$