(x-5)(45-1x-5)=4(45-x-5))

Solution for (x-5)(45-1x-5)=4(45-x-5)) equation:

(x-5)(45-1x-5)=4(45-x-5))

We move all terms to the left:

(x-5)(45-1x-5)-(4(45-x-5)))=0

We add all the numbers together, and all the variables

(x-5)(-1x+40)-(4(-1x+40)))=0

We multiply parentheses ..

(-1x^2+40x+5x-200)-(4(-1x+40)))=0


We calculate terms in parentheses: -(4(-1x+40))), so:

4(-1x+40))

We multiply parentheses

-4x+

We add all the numbers together, and all the variables

-4x

Back to the equation:

-(-4x)


We get rid of parentheses

-1x^2+40x+5x+4x-200=0

We add all the numbers together, and all the variables

-1x^2+49x-200=0

a = -1; b = 49; c = -200;
Δ = b2-4ac
Δ = 492-4·(-1)·(-200)
Δ = 1601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-\sqrt{1601}}{2*-1}=\frac{-49-\sqrt{1601}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+\sqrt{1601}}{2*-1}=\frac{-49+\sqrt{1601}}{-2}
$