0.5x^2-82x+432=0

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Solution for 0.5x^2-82x+432=0 equation:



0.5x^2-82x+432=0
a = 0.5; b = -82; c = +432;
Δ = b2-4ac
Δ = -822-4·0.5·432
Δ = 5860
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:
$\sqrt{\Delta}=\sqrt{5860}=\sqrt{4*1465}=\sqrt{4}*\sqrt{1465}=2\sqrt{1465}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-2\sqrt{1465}}{2*0.5}=\frac{82-2\sqrt{1465}}{1} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+2\sqrt{1465}}{2*0.5}=\frac{82+2\sqrt{1465}}{1} $

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