1=11x2+10x

Solution for 1=11x2+10x equation:

1=11x^2+10x

We move all terms to the left:

1-(11x^2+10x)=0

We get rid of parentheses

-11x^2-10x+1=0

a = -11; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·(-11)·1
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-12}{2*-11}=\frac{-2}{-22}
=1/11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+12}{2*-11}=\frac{22}{-22}
=-1
$