(x-1)(x+12)=17x

Solution for (x-1)(x+12)=17x equation:

(x-1)(x+12)=17x

We move all terms to the left:

(x-1)(x+12)-(17x)=0

We add all the numbers together, and all the variables

-17x+(x-1)(x+12)=0

We multiply parentheses ..

(+x^2+12x-1x-12)-17x=0

We get rid of parentheses

x^2+12x-1x-17x-12=0

We add all the numbers together, and all the variables

x^2-6x-12=0

a = 1; b = -6; c = -12;
Δ = b2-4ac
Δ = -62-4·1·(-12)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{21}}{2*1}=\frac{6-2\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{21}}{2*1}=\frac{6+2\sqrt{21}}{2}
$