x^2-24x+68=0

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Solution for x^2-24x+68=0 equation:



x^2-24x+68=0
a = 1; b = -24; c = +68;
Δ = b2-4ac
Δ = -242-4·1·68
Δ = 304
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:
$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{19}}{2*1}=\frac{24-4\sqrt{19}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{19}}{2*1}=\frac{24+4\sqrt{19}}{2} $

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