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12.31x^2-2.308x-1.5=0
a = 12.31; b = -2.308; c = -1.5;
Δ = b2-4ac
Δ = -2.3082-4·12.31·(-1.5)
Δ = 79.186864
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2.308)-\sqrt{79.186864}}{2*12.31}=\frac{2.308-\sqrt{79.186864}}{24.62} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.308)+\sqrt{79.186864}}{2*12.31}=\frac{2.308+\sqrt{79.186864}}{24.62} $
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