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5x^2-64x+14=0
a = 5; b = -64; c = +14;
Δ = b2-4ac
Δ = -642-4·5·14
Δ = 3816
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3816}=\sqrt{36*106}=\sqrt{36}*\sqrt{106}=6\sqrt{106}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-6\sqrt{106}}{2*5}=\frac{64-6\sqrt{106}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+6\sqrt{106}}{2*5}=\frac{64+6\sqrt{106}}{10} $
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