40y-7=12y^2

Solution for 40y-7=12y^2 equation:

40y-7=12y^2

We move all terms to the left:

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

determiningTheFunctionDomain
-12y^2+40y-7=0

a = -12; b = 40; c = -7;
Δ = b2-4ac
Δ = 402-4·(-12)·(-7)
Δ = 1264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1264}=\sqrt{16*79}=\sqrt{16}*\sqrt{79}=4\sqrt{79}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{79}}{2*-12}=\frac{-40-4\sqrt{79}}{-24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{79}}{2*-12}=\frac{-40+4\sqrt{79}}{-24}
$