(x+6)(7x)=(x+6)(14)

Solution for (x+6)(7x)=(x+6)(14) equation:

(x+6)(7x)=(x+6)(14)

We move all terms to the left:

(x+6)(7x)-((x+6)(14))=0

We multiply parentheses

7x^2+42x-((x+6)14)=0


We calculate terms in parentheses: -((x+6)14), so:

(x+6)14

We multiply parentheses

14x+84

Back to the equation:

-(14x+84)


We get rid of parentheses

7x^2+42x-14x-84=0

We add all the numbers together, and all the variables

7x^2+28x-84=0

a = 7; b = 28; c = -84;
Δ = b2-4ac
Δ = 282-4·7·(-84)
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-56}{2*7}=\frac{-84}{14}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+56}{2*7}=\frac{28}{14}
=2
$