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24x^2+46x+21=0
a = 24; b = 46; c = +21;
Δ = b2-4ac
Δ = 462-4·24·21
Δ = 100
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{100}=10$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-10}{2*24}=\frac{-56}{48} =-1+1/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+10}{2*24}=\frac{-36}{48} =-3/4 $
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