(x+1)(x+10)=112

Solution for (x+1)(x+10)=112 equation:

(x+1)(x+10)=112

We move all terms to the left:

(x+1)(x+10)-(112)=0

We multiply parentheses ..

(+x^2+10x+x+10)-112=0

We get rid of parentheses

x^2+10x+x+10-112=0

We add all the numbers together, and all the variables

x^2+11x-102=0

a = 1; b = 11; c = -102;
Δ = b2-4ac
Δ = 112-4·1·(-102)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-23}{2*1}=\frac{-34}{2}
=-17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+23}{2*1}=\frac{12}{2}
=6
$