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6x^2+13.5x+6.75=0
a = 6; b = 13.5; c = +6.75;
Δ = b2-4ac
Δ = 13.52-4·6·6.75
Δ = 20.25
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13.5)-\sqrt{20.25}}{2*6}=\frac{-13.5-\sqrt{20.25}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13.5)+\sqrt{20.25}}{2*6}=\frac{-13.5+\sqrt{20.25}}{12} $
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