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2x^2+3x=74

We move all terms to the left:

2x^2+3x-(74)=0

a = 2; b = 3; c = -74;

Δ = b^{2}-4ac

Δ = 3^{2}-4·2·(-74)

Δ = 601

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{-(3)-\sqrt{601}}{2*2}=\frac{-3-\sqrt{601}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{601}}{2*2}=\frac{-3+\sqrt{601}}{4} $

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