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30x^2-31x=24
We move all terms to the left:
30x^2-31x-(24)=0
a = 30; b = -31; c = -24;
Δ = b2-4ac
Δ = -312-4·30·(-24)
Δ = 3841
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{-(-31)-\sqrt{3841}}{2*30}=\frac{31-\sqrt{3841}}{60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{3841}}{2*30}=\frac{31+\sqrt{3841}}{60} $
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