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5x^2+0x-13=0
We add all the numbers together, and all the variables
5x^2+x-13=0
a = 5; b = 1; c = -13;
Δ = b2-4ac
Δ = 12-4·5·(-13)
Δ = 261
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{29}}{2*5}=\frac{-1-3\sqrt{29}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{29}}{2*5}=\frac{-1+3\sqrt{29}}{10} $
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