x+5x2=71

Solution for x+5x2=71 equation:

x+5x^2=71

We move all terms to the left:

x+5x^2-(71)=0

a = 5; b = 1; c = -71;
Δ = b2-4ac
Δ = 12-4·5·(-71)
Δ = 1421
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:

$\sqrt{\Delta}=\sqrt{1421}=\sqrt{49*29}=\sqrt{49}*\sqrt{29}=7\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7\sqrt{29}}{2*5}=\frac{-1-7\sqrt{29}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7\sqrt{29}}{2*5}=\frac{-1+7\sqrt{29}}{10}
$