7-x(5x+2)=3-x(4-x)

Solution for 7-x(5x+2)=3-x(4-x) equation:

7-x(5x+2)=3-x(4-x)

We move all terms to the left:

7-x(5x+2)-(3-x(4-x))=0

We add all the numbers together, and all the variables

-x(5x+2)-(3-x(-1x+4))+7=0

We multiply parentheses

-5x^2-2x-(3-x(-1x+4))+7=0


We calculate terms in parentheses: -(3-x(-1x+4)), so:

3-x(-1x+4)

determiningTheFunctionDomain
-x(-1x+4)+3

We multiply parentheses

1x^2-4x+3

We add all the numbers together, and all the variables

x^2-4x+3

Back to the equation:

-(x^2-4x+3)


We get rid of parentheses

-5x^2-x^2-2x+4x-3+7=0

We add all the numbers together, and all the variables

-6x^2+2x+4=0

a = -6; b = 2; c = +4;
Δ = b2-4ac
Δ = 22-4·(-6)·4
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10}{2*-6}=\frac{-12}{-12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*-6}=\frac{8}{-12}
=-2/3
$