X(11x+1)=10

Solution for X(11x+1)=10 equation:

X(11X+1)=10

We move all terms to the left:

X(11X+1)-(10)=0

We multiply parentheses

11X^2+X-10=0

a = 11; b = 1; c = -10;
Δ = b2-4ac
Δ = 12-4·11·(-10)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-21}{2*11}=\frac{-22}{22}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+21}{2*11}=\frac{20}{22}
=10/11
$