7x(x+8)=-7

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

7x(x+8)=-7

We move all terms to the left:

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

We add all the numbers together, and all the variables

7x(x+8)+7=0

We multiply parentheses

7x^2+56x+7=0

a = 7; b = 56; c = +7;
Δ = b2-4ac
Δ = 562-4·7·7
Δ = 2940
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2940}=\sqrt{196*15}=\sqrt{196}*\sqrt{15}=14\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-14\sqrt{15}}{2*7}=\frac{-56-14\sqrt{15}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+14\sqrt{15}}{2*7}=\frac{-56+14\sqrt{15}}{14}
$