5x=1+6x2

Solution for 5x=1+6x2 equation:

5x=1+6x^2

We move all terms to the left:

5x-(1+6x^2)=0

We get rid of parentheses

-6x^2+5x-1=0

a = -6; b = 5; c = -1;
Δ = b2-4ac
Δ = 52-4·(-6)·(-1)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-1}{2*-6}=\frac{-6}{-12}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+1}{2*-6}=\frac{-4}{-12}
=1/3
$