x(x-1)-7x=18-5(x+4)

Solution for x(x-1)-7x=18-5(x+4) equation:

x(x-1)-7x=18-5(x+4)

We move all terms to the left:

x(x-1)-7x-(18-5(x+4))=0

We add all the numbers together, and all the variables

-7x+x(x-1)-(18-5(x+4))=0

We multiply parentheses

x^2-7x-1x-(18-5(x+4))=0


We calculate terms in parentheses: -(18-5(x+4)), so:

18-5(x+4)

determiningTheFunctionDomain
-5(x+4)+18

We multiply parentheses

-5x-20+18

We add all the numbers together, and all the variables

-5x-2

Back to the equation:

-(-5x-2)


We add all the numbers together, and all the variables

x^2-8x-(-5x-2)=0

We get rid of parentheses

x^2-8x+5x+2=0

We add all the numbers together, and all the variables

x^2-3x+2=0

a = 1; b = -3; c = +2;
Δ = b2-4ac
Δ = -32-4·1·2
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-1}{2*1}=\frac{2}{2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+1}{2*1}=\frac{4}{2}
=2
$