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5x^2-x-3=0
We add all the numbers together, and all the variables
5x^2-1x-3=0
a = 5; b = -1; c = -3;
Δ = b2-4ac
Δ = -12-4·5·(-3)
Δ = 61
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{-(-1)-\sqrt{61}}{2*5}=\frac{1-\sqrt{61}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{61}}{2*5}=\frac{1+\sqrt{61}}{10} $
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