x=11x2-21x-3

Solution for x=11x2-21x-3 equation:

x=11x^2-21x-3

We move all terms to the left:

x-(11x^2-21x-3)=0

We get rid of parentheses

-11x^2+x+21x+3=0

We add all the numbers together, and all the variables

-11x^2+22x+3=0

a = -11; b = 22; c = +3;
Δ = b2-4ac
Δ = 222-4·(-11)·3
Δ = 616
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{616}=\sqrt{4*154}=\sqrt{4}*\sqrt{154}=2\sqrt{154}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{154}}{2*-11}=\frac{-22-2\sqrt{154}}{-22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{154}}{2*-11}=\frac{-22+2\sqrt{154}}{-22}
$