-208,21=45,522*x-2,529*x^2

Solution for -208,21=45,522*x-2,529*x^2 equation:

-208.21=45.522x-2.529x^2

We move all terms to the left:

-208.21-(45.522x-2.529x^2)=0

We get rid of parentheses

2.529x^2-45.522x-208.21=0

a = 2.529; b = -45.522; c = -208.21;
Δ = b2-4ac
Δ = -45.5222-4·2.529·(-208.21)
Δ = 4178.504844
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{-(-45.522)-\sqrt{4178.504844}}{2*2.529}=\frac{45.522-\sqrt{4178.504844}}{5.058}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45.522)+\sqrt{4178.504844}}{2*2.529}=\frac{45.522+\sqrt{4178.504844}}{5.058}
$