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2x^2+5x-8=0

a = 2; b = 5; c = -8;

Δ = b^{2}-4ac

Δ = 5^{2}-4·2·(-8)

Δ = 89

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{-(5)-\sqrt{89}}{2*2}=\frac{-5-\sqrt{89}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{89}}{2*2}=\frac{-5+\sqrt{89}}{4} $

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