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x+5x^2-7=13
We move all terms to the left:
x+5x^2-7-(13)=0
We add all the numbers together, and all the variables
5x^2+x-20=0
a = 5; b = 1; c = -20;
Δ = b2-4ac
Δ = 12-4·5·(-20)
Δ = 401
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{401}}{2*5}=\frac{-1-\sqrt{401}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{401}}{2*5}=\frac{-1+\sqrt{401}}{10} $
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