x+5x^2=22

Solution for x+5x^2=22 equation:

x+5x^2=22

We move all terms to the left:

x+5x^2-(22)=0

a = 5; b = 1; c = -22;
Δ = b2-4ac
Δ = 12-4·5·(-22)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-21}{2*5}=\frac{-22}{10}
=-2+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+21}{2*5}=\frac{20}{10}
=2
$