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5t^2-7t-12=0
a = 5; b = -7; c = -12;
Δ = b2-4ac
Δ = -72-4·5·(-12)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{289}=17$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-17}{2*5}=\frac{-10}{10} =-1 $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+17}{2*5}=\frac{24}{10} =2+2/5 $
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