x(x-5)=4(5-x)

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

x(x-5)=4(5-x)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


We calculate terms in parentheses: -(4(-1x+5)), so:

4(-1x+5)

We multiply parentheses

-4x+20

Back to the equation:

-(-4x+20)


We get rid of parentheses

x^2-5x+4x-20=0

We add all the numbers together, and all the variables

x^2-1x-20=0

a = 1; b = -1; c = -20;
Δ = b2-4ac
Δ = -12-4·1·(-20)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-9}{2*1}=\frac{-8}{2}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9}{2*1}=\frac{10}{2}
=5
$