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1.5x^2-6x+3=0
a = 1.5; b = -6; c = +3;
Δ = b2-4ac
Δ = -62-4·1.5·3
Δ = 18
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{18}=\sqrt{9*2}=\sqrt{9}*\sqrt{2}=3\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-3\sqrt{2}}{2*1.5}=\frac{6-3\sqrt{2}}{3} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+3\sqrt{2}}{2*1.5}=\frac{6+3\sqrt{2}}{3} $
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