(x-8)(x-4)=3x-18

Solution for (x-8)(x-4)=3x-18 equation:

(x-8)(x-4)=3x-18

We move all terms to the left:

(x-8)(x-4)-(3x-18)=0

We get rid of parentheses

(x-8)(x-4)-3x+18=0

We multiply parentheses ..

(+x^2-4x-8x+32)-3x+18=0

We get rid of parentheses

x^2-4x-8x-3x+32+18=0

We add all the numbers together, and all the variables

x^2-15x+50=0

a = 1; b = -15; c = +50;
Δ = b2-4ac
Δ = -152-4·1·50
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{-(-15)-5}{2*1}=\frac{10}{2}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5}{2*1}=\frac{20}{2}
=10
$