6x(x+7)=(6x+42)

Solution for 6x(x+7)=(6x+42) equation:

6x(x+7)=(6x+42)

We move all terms to the left:

6x(x+7)-((6x+42))=0

We multiply parentheses

6x^2+42x-((6x+42))=0


We calculate terms in parentheses: -((6x+42)), so:

(6x+42)

We get rid of parentheses

6x+42

Back to the equation:

-(6x+42)


We get rid of parentheses

6x^2+42x-6x-42=0

We add all the numbers together, and all the variables

6x^2+36x-42=0

a = 6; b = 36; c = -42;
Δ = b2-4ac
Δ = 362-4·6·(-42)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-48}{2*6}=\frac{-84}{12}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+48}{2*6}=\frac{12}{12}
=1
$