1+12y^2=7y

Solution for 1+12y^2=7y equation:

1+12y^2=7y

We move all terms to the left:

1+12y^2-(7y)=0

a = 12; b = -7; c = +1;
Δ = b2-4ac
Δ = -72-4·12·1
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-1}{2*12}=\frac{6}{24}
=1/4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+1}{2*12}=\frac{8}{24}
=1/3
$