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1.5x^2+5x-84=0
a = 1.5; b = 5; c = -84;
Δ = b2-4ac
Δ = 52-4·1.5·(-84)
Δ = 529
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{529}=23$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-23}{2*1.5}=\frac{-28}{3} =-9+1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+23}{2*1.5}=\frac{18}{3} =6 $
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