5y+12=13y^2

Solution for 5y+12=13y^2 equation:

5y+12=13y^2

We move all terms to the left:

5y+12-(13y^2)=0

determiningTheFunctionDomain
-13y^2+5y+12=0

a = -13; b = 5; c = +12;
Δ = b2-4ac
Δ = 52-4·(-13)·12
Δ = 649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{649}}{2*-13}=\frac{-5-\sqrt{649}}{-26}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{649}}{2*-13}=\frac{-5+\sqrt{649}}{-26}
$