5323=x(0,73x+440)

Solution for 5323=x(0,73x+440) equation:

5323=x(0.73x+440)

We move all terms to the left:

5323-(x(0.73x+440))=0


We calculate terms in parentheses: -(x(0.73x+440)), so:

x(0.73x+440)

We multiply parentheses

0x^2+440x

We add all the numbers together, and all the variables

x^2+440x

Back to the equation:

-(x^2+440x)


We get rid of parentheses

-x^2-440x+5323=0

We add all the numbers together, and all the variables

-1x^2-440x+5323=0

a = -1; b = -440; c = +5323;
Δ = b2-4ac
Δ = -4402-4·(-1)·5323
Δ = 214892
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:

$\sqrt{\Delta}=\sqrt{214892}=\sqrt{4*53723}=\sqrt{4}*\sqrt{53723}=2\sqrt{53723}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-440)-2\sqrt{53723}}{2*-1}=\frac{440-2\sqrt{53723}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-440)+2\sqrt{53723}}{2*-1}=\frac{440+2\sqrt{53723}}{-2}
$