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24x^2+3x-21=0
a = 24; b = 3; c = -21;
Δ = b2-4ac
Δ = 32-4·24·(-21)
Δ = 2025
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{2025}=45$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-45}{2*24}=\frac{-48}{48} =-1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+45}{2*24}=\frac{42}{48} =7/8 $
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