10x-1=5x^2

Solution for 10x-1=5x^2 equation:

10x-1=5x^2

We move all terms to the left:

10x-1-(5x^2)=0

determiningTheFunctionDomain
-5x^2+10x-1=0

a = -5; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·(-5)·(-1)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{5}}{2*-5}=\frac{-10-4\sqrt{5}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{5}}{2*-5}=\frac{-10+4\sqrt{5}}{-10}
$