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4x^2-82x+414=0
a = 4; b = -82; c = +414;
Δ = b2-4ac
Δ = -822-4·4·414
Δ = 100
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{100}=10$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-10}{2*4}=\frac{72}{8} =9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+10}{2*4}=\frac{92}{8} =11+1/2 $
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