10732=4.61x2+43.4x+1620

Solution for 10732=4.61x2+43.4x+1620 equation:

10732=4.61x^2+43.4x+1620

We move all terms to the left:

10732-(4.61x^2+43.4x+1620)=0

We get rid of parentheses

-4.61x^2-43.4x-1620+10732=0

We add all the numbers together, and all the variables

-4.61x^2-43.4x+9112=0

a = -4.61; b = -43.4; c = +9112;
Δ = b2-4ac
Δ = -43.42-4·(-4.61)·9112
Δ = 169908.84
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{-(-43.4)-\sqrt{169908.84}}{2*-4.61}=\frac{43.4-\sqrt{169908.84}}{-9.22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43.4)+\sqrt{169908.84}}{2*-4.61}=\frac{43.4+\sqrt{169908.84}}{-9.22}
$