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6w^2-23w+7=0
a = 6; b = -23; c = +7;
Δ = b2-4ac
Δ = -232-4·6·7
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{361}=19$$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-19}{2*6}=\frac{4}{12} =1/3 $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+19}{2*6}=\frac{42}{12} =3+1/2 $
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