3x=-1+5x^2

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

3x=-1+5x^2

We move all terms to the left:

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

We get rid of parentheses

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

a = -5; b = 3; c = +1;
Δ = b2-4ac
Δ = 32-4·(-5)·1
Δ = 29
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{-(3)-\sqrt{29}}{2*-5}=\frac{-3-\sqrt{29}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{29}}{2*-5}=\frac{-3+\sqrt{29}}{-10}
$