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5x^2-18x+3=0
a = 5; b = -18; c = +3;
Δ = b2-4ac
Δ = -182-4·5·3
Δ = 264
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{66}}{2*5}=\frac{18-2\sqrt{66}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{66}}{2*5}=\frac{18+2\sqrt{66}}{10} $
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