2x+1=5x^2

Solution for 2x+1=5x^2 equation:

2x+1=5x^2

We move all terms to the left:

2x+1-(5x^2)=0

determiningTheFunctionDomain
-5x^2+2x+1=0

a = -5; b = 2; c = +1;
Δ = b2-4ac
Δ = 22-4·(-5)·1
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{6}}{2*-5}=\frac{-2-2\sqrt{6}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{6}}{2*-5}=\frac{-2+2\sqrt{6}}{-10}
$