x^2+2x+1=17x-55

Solution for x^2+2x+1=17x-55 equation:

x^2+2x+1=17x-55

We move all terms to the left:

x^2+2x+1-(17x-55)=0

We get rid of parentheses

x^2+2x-17x+55+1=0

We add all the numbers together, and all the variables

x^2-15x+56=0

a = 1; b = -15; c = +56;
Δ = b2-4ac
Δ = -152-4·1·56
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-1}{2*1}=\frac{14}{2}
=7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+1}{2*1}=\frac{16}{2}
=8
$