55=x^2+8x+7

Solution for 55=x^2+8x+7 equation:

55=x^2+8x+7

We move all terms to the left:

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

We get rid of parentheses

-x^2-8x-7+55=0

We add all the numbers together, and all the variables

-1x^2-8x+48=0

a = -1; b = -8; c = +48;
Δ = b2-4ac
Δ = -82-4·(-1)·48
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16}{2*-1}=\frac{-8}{-2}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16}{2*-1}=\frac{24}{-2}
=-12
$