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-x^2+6x+41=0
We add all the numbers together, and all the variables
-1x^2+6x+41=0
a = -1; b = 6; c = +41;
Δ = b2-4ac
Δ = 62-4·(-1)·41
Δ = 200
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-10\sqrt{2}}{2*-1}=\frac{-6-10\sqrt{2}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+10\sqrt{2}}{2*-1}=\frac{-6+10\sqrt{2}}{-2} $
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