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

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

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

We move all terms to the left:

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

We multiply parentheses

4x^2+28x-((3x-3)(x+7))=0

We multiply parentheses ..

4x^2-((+3x^2+21x-3x-21))+28x=0


We calculate terms in parentheses: -((+3x^2+21x-3x-21)), so:

(+3x^2+21x-3x-21)

We get rid of parentheses

3x^2+21x-3x-21

We add all the numbers together, and all the variables

3x^2+18x-21

Back to the equation:

-(3x^2+18x-21)


We add all the numbers together, and all the variables

4x^2+28x-(3x^2+18x-21)=0

We get rid of parentheses

4x^2-3x^2+28x-18x+21=0

We add all the numbers together, and all the variables

x^2+10x+21=0

a = 1; b = 10; c = +21;
Δ = b2-4ac
Δ = 102-4·1·21
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4}{2*1}=\frac{-14}{2}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4}{2*1}=\frac{-6}{2}
=-3
$