(X-5)(x-3)=25(x-5)

Solution for (X-5)(x-3)=25(x-5) equation:

(X-5)(X-3)=25(X-5)

We move all terms to the left:

(X-5)(X-3)-(25(X-5))=0

We multiply parentheses ..

(+X^2-3X-5X+15)-(25(X-5))=0


We calculate terms in parentheses: -(25(X-5)), so:

25(X-5)

We multiply parentheses

25X-125

Back to the equation:

-(25X-125)


We get rid of parentheses

X^2-3X-5X-25X+15+125=0

We add all the numbers together, and all the variables

X^2-33X+140=0

a = 1; b = -33; c = +140;
Δ = b2-4ac
Δ = -332-4·1·140
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-23}{2*1}=\frac{10}{2}
=5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+23}{2*1}=\frac{56}{2}
=28
$