3-2(1-x)=5+7x(x-3)

Solution for 3-2(1-x)=5+7x(x-3) equation:

3-2(1-x)=5+7x(x-3)

We move all terms to the left:

3-2(1-x)-(5+7x(x-3))=0

We add all the numbers together, and all the variables

-2(-1x+1)-(5+7x(x-3))+3=0

We multiply parentheses

2x-(5+7x(x-3))-2+3=0


We calculate terms in parentheses: -(5+7x(x-3)), so:

5+7x(x-3)

determiningTheFunctionDomain
7x(x-3)+5

We multiply parentheses

7x^2-21x+5

Back to the equation:

-(7x^2-21x+5)


We add all the numbers together, and all the variables

2x-(7x^2-21x+5)+1=0

We get rid of parentheses

-7x^2+2x+21x-5+1=0

We add all the numbers together, and all the variables

-7x^2+23x-4=0

a = -7; b = 23; c = -4;
Δ = b2-4ac
Δ = 232-4·(-7)·(-4)
Δ = 417
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-\sqrt{417}}{2*-7}=\frac{-23-\sqrt{417}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{417}}{2*-7}=\frac{-23+\sqrt{417}}{-14}
$