12y^2+5y-2=30

Solution for 12y^2+5y-2=30 equation:

12y^2+5y-2=30

We move all terms to the left:

12y^2+5y-2-(30)=0

We add all the numbers together, and all the variables

12y^2+5y-32=0

a = 12; b = 5; c = -32;
Δ = b2-4ac
Δ = 52-4·12·(-32)
Δ = 1561
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{1561}}{2*12}=\frac{-5-\sqrt{1561}}{24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{1561}}{2*12}=\frac{-5+\sqrt{1561}}{24}
$