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-24x^2-22x-3=0
a = -24; b = -22; c = -3;
Δ = b2-4ac
Δ = -222-4·(-24)·(-3)
Δ = 196
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{196}=14$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-14}{2*-24}=\frac{8}{-48} =-1/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+14}{2*-24}=\frac{36}{-48} =-3/4 $
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