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5x^2+18x-13=0
a = 5; b = 18; c = -13;
Δ = b2-4ac
Δ = 182-4·5·(-13)
Δ = 584
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{584}=\sqrt{4*146}=\sqrt{4}*\sqrt{146}=2\sqrt{146}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{146}}{2*5}=\frac{-18-2\sqrt{146}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{146}}{2*5}=\frac{-18+2\sqrt{146}}{10} $
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