4.4*10^-4(.53-x)-x^2=0

Solution for 4.4*10^-4(.53-x)-x^2=0 equation:

4.4*10^-4(.53-x)-x^2=0

We add all the numbers together, and all the variables

-x^2-4(-1x+0.53)+4.4*10^=0

We add all the numbers together, and all the variables

-1x^2-4(-1x+0.53)=0

We multiply parentheses

-1x^2+4x-2.12=0

a = -1; b = 4; c = -2.12;
Δ = b2-4ac
Δ = 42-4·(-1)·(-2.12)
Δ = 7.52
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{-(4)-\sqrt{7.52}}{2*-1}=\frac{-4-\sqrt{7.52}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+\sqrt{7.52}}{2*-1}=\frac{-4+\sqrt{7.52}}{-2}
$