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38x^2-3x-11=0
a = 38; b = -3; c = -11;
Δ = b2-4ac
Δ = -32-4·38·(-11)
Δ = 1681
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{1681}=41$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-41}{2*38}=\frac{-38}{76} =-1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+41}{2*38}=\frac{44}{76} =11/19 $
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