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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} $
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