7x+3=-4+7x(x+1)

Solution for 7x+3=-4+7x(x+1) equation:

7x+3=-4+7x(x+1)

We move all terms to the left:

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


We calculate terms in parentheses: -(-4+7x(x+1)), so:

-4+7x(x+1)

determiningTheFunctionDomain
7x(x+1)-4

We multiply parentheses

7x^2+7x-4

Back to the equation:

-(7x^2+7x-4)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-7x^2+7=0

a = -7; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-7)·7
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14}{2*-7}=\frac{-14}{-14}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14}{2*-7}=\frac{14}{-14}
=-1
$