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1.5x^2-24x-15=0
a = 1.5; b = -24; c = -15;
Δ = b2-4ac
Δ = -242-4·1.5·(-15)
Δ = 666
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{666}=\sqrt{9*74}=\sqrt{9}*\sqrt{74}=3\sqrt{74}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-3\sqrt{74}}{2*1.5}=\frac{24-3\sqrt{74}}{3} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+3\sqrt{74}}{2*1.5}=\frac{24+3\sqrt{74}}{3} $
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