5x-1=3x^2

Solution for 5x-1=3x^2 equation:

5x-1=3x^2

We move all terms to the left:

5x-1-(3x^2)=0

determiningTheFunctionDomain
-3x^2+5x-1=0

a = -3; b = 5; c = -1;
Δ = b2-4ac
Δ = 52-4·(-3)·(-1)
Δ = 13
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{-(5)-\sqrt{13}}{2*-3}=\frac{-5-\sqrt{13}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{13}}{2*-3}=\frac{-5+\sqrt{13}}{-6}
$