x(x-23)=17(x-23)

Solution for x(x-23)=17(x-23) equation:

x(x-23)=17(x-23)

We move all terms to the left:

x(x-23)-(17(x-23))=0

We multiply parentheses

x^2-23x-(17(x-23))=0


We calculate terms in parentheses: -(17(x-23)), so:

17(x-23)

We multiply parentheses

17x-391

Back to the equation:

-(17x-391)


We get rid of parentheses

x^2-23x-17x+391=0

We add all the numbers together, and all the variables

x^2-40x+391=0

a = 1; b = -40; c = +391;
Δ = b2-4ac
Δ = -402-4·1·391
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-6}{2*1}=\frac{34}{2}
=17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+6}{2*1}=\frac{46}{2}
=23
$