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x+5x^2=19
We move all terms to the left:
x+5x^2-(19)=0
a = 5; b = 1; c = -19;
Δ = b2-4ac
Δ = 12-4·5·(-19)
Δ = 381
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{381}}{2*5}=\frac{-1-\sqrt{381}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{381}}{2*5}=\frac{-1+\sqrt{381}}{10} $
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