(X-5)(45-x)=4(x-5)

Solution for (X-5)(45-x)=4(x-5) equation:

(X-5)(45-X)=4(X-5)

We move all terms to the left:

(X-5)(45-X)-(4(X-5))=0

We add all the numbers together, and all the variables

(X-5)(-1X+45)-(4(X-5))=0

We multiply parentheses ..

(-1X^2+45X+5X-225)-(4(X-5))=0


We calculate terms in parentheses: -(4(X-5)), so:

4(X-5)

We multiply parentheses

4X-20

Back to the equation:

-(4X-20)


We get rid of parentheses

-1X^2+45X+5X-4X-225+20=0

We add all the numbers together, and all the variables

-1X^2+46X-205=0

a = -1; b = 46; c = -205;
Δ = b2-4ac
Δ = 462-4·(-1)·(-205)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-36}{2*-1}=\frac{-82}{-2}
=+41
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+36}{2*-1}=\frac{-10}{-2}
=+5
$