192.7=x(x-22.1)

Solution for 192.7=x(x-22.1) equation:

192.7=x(x-22.1)

We move all terms to the left:

192.7-(x(x-22.1))=0


We calculate terms in parentheses: -(x(x-22.1)), so:

x(x-22.1)

We multiply parentheses

x^2-22.1x

Back to the equation:

-(x^2-22.1x)


We get rid of parentheses

-x^2+22.1x+192.7=0

We add all the numbers together, and all the variables

-1x^2+22.1x+192.7=0

a = -1; b = 22.1; c = +192.7;
Δ = b2-4ac
Δ = 22.12-4·(-1)·192.7
Δ = 1259.21
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22.1)-\sqrt{1259.21}}{2*-1}=\frac{-22.1-\sqrt{1259.21}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22.1)+\sqrt{1259.21}}{2*-1}=\frac{-22.1+\sqrt{1259.21}}{-2}
$