5x(x+-1)+5=7+x(1-2x)

Solution for 5x(x+-1)+5=7+x(1-2x) equation:

5x(x+-1)+5=7+x(1-2x)

We move all terms to the left:

5x(x+-1)+5-(7+x(1-2x))=0

We add all the numbers together, and all the variables

5x(x-1)-(7+x(-2x+1))+5=0

We multiply parentheses

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


We calculate terms in parentheses: -(7+x(-2x+1)), so:

7+x(-2x+1)

determiningTheFunctionDomain
x(-2x+1)+7

We multiply parentheses

-2x^2+x+7

Back to the equation:

-(-2x^2+x+7)


We get rid of parentheses

5x^2+2x^2-x-5x-7+5=0

We add all the numbers together, and all the variables

7x^2-6x-2=0

a = 7; b = -6; c = -2;
Δ = b2-4ac
Δ = -62-4·7·(-2)
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{23}}{2*7}=\frac{6-2\sqrt{23}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{23}}{2*7}=\frac{6+2\sqrt{23}}{14}
$