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6x^2+23x+21=0
a = 6; b = 23; c = +21;
Δ = b2-4ac
Δ = 232-4·6·21
Δ = 25
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{25}=5$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-5}{2*6}=\frac{-28}{12} =-2+1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+5}{2*6}=\frac{-18}{12} =-1+1/2 $
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