0.09=x(x+21.74)

Solution for 0.09=x(x+21.74) equation:

0.09=x(x+21.74)

We move all terms to the left:

0.09-(x(x+21.74))=0


We calculate terms in parentheses: -(x(x+21.74)), so:

x(x+21.74)

We multiply parentheses

x^2+21.74x

Back to the equation:

-(x^2+21.74x)


We get rid of parentheses

-x^2-21.74x+0.09=0

We add all the numbers together, and all the variables

-1x^2-21.74x+0.09=0

a = -1; b = -21.74; c = +0.09;
Δ = b2-4ac
Δ = -21.742-4·(-1)·0.09
Δ = 472.9876
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{-(-21.74)-\sqrt{472.9876}}{2*-1}=\frac{21.74-\sqrt{472.9876}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21.74)+\sqrt{472.9876}}{2*-1}=\frac{21.74+\sqrt{472.9876}}{-2}
$