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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

5x-(7+x(-2x+1))-5+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 add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2+4x-7=0

a = 2; b = 4; c = -7;
Δ = b2-4ac
Δ = 42-4·2·(-7)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6\sqrt{2}}{2*2}=\frac{-4-6\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6\sqrt{2}}{2*2}=\frac{-4+6\sqrt{2}}{4}
$