5(x-36)-(x+36)=48-x(x-48)

Solution for 5(x-36)-(x+36)=48-x(x-48) equation:

5(x-36)-(x+36)=48-x(x-48)

We move all terms to the left:

5(x-36)-(x+36)-(48-x(x-48))=0

We multiply parentheses

5x-(x+36)-(48-x(x-48))-180=0

We get rid of parentheses

5x-x-(48-x(x-48))-36-180=0


We calculate terms in parentheses: -(48-x(x-48)), so:

48-x(x-48)

determiningTheFunctionDomain
-x(x-48)+48

We multiply parentheses

-x^2+48x+48

We add all the numbers together, and all the variables

-1x^2+48x+48

Back to the equation:

-(-1x^2+48x+48)


We add all the numbers together, and all the variables

-(-1x^2+48x+48)+4x-216=0

We get rid of parentheses

1x^2-48x+4x-48-216=0

We add all the numbers together, and all the variables

x^2-44x-264=0

a = 1; b = -44; c = -264;
Δ = b2-4ac
Δ = -442-4·1·(-264)
Δ = 2992
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2992}=\sqrt{16*187}=\sqrt{16}*\sqrt{187}=4\sqrt{187}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{187}}{2*1}=\frac{44-4\sqrt{187}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{187}}{2*1}=\frac{44+4\sqrt{187}}{2}
$