12y2+40y=7

Solution for 12y2+40y=7 equation:

12y^2+40y=7

We move all terms to the left:

12y^2+40y-(7)=0

a = 12; b = 40; c = -7;
Δ = b2-4ac
Δ = 402-4·12·(-7)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-44}{2*12}=\frac{-84}{24}
=-3+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+44}{2*12}=\frac{4}{24}
=1/6
$