8x(x+7)=(x+7)

Solution for 8x(x+7)=(x+7) equation:

8x(x+7)=(x+7)

We move all terms to the left:

8x(x+7)-((x+7))=0

We multiply parentheses

8x^2+56x-((x+7))=0


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

(x+7)

We get rid of parentheses

x+7

Back to the equation:

-(x+7)


We get rid of parentheses

8x^2+56x-x-7=0

We add all the numbers together, and all the variables

8x^2+55x-7=0

a = 8; b = 55; c = -7;
Δ = b2-4ac
Δ = 552-4·8·(-7)
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-57}{2*8}=\frac{-112}{16}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+57}{2*8}=\frac{2}{16}
=1/8
$