(x-1)(x-8)=5x

Solution for (x-1)(x-8)=5x equation:

(x-1)(x-8)=5x

We move all terms to the left:

(x-1)(x-8)-(5x)=0

We add all the numbers together, and all the variables

-5x+(x-1)(x-8)=0

We multiply parentheses ..

(+x^2-8x-1x+8)-5x=0

We get rid of parentheses

x^2-8x-1x-5x+8=0

We add all the numbers together, and all the variables

x^2-14x+8=0

a = 1; b = -14; c = +8;
Δ = b2-4ac
Δ = -142-4·1·8
Δ = 164
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{41}}{2*1}=\frac{14-2\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{41}}{2*1}=\frac{14+2\sqrt{41}}{2}
$