4y^2+24y=37

Solution for 4y^2+24y=37 equation:

4y^2+24y=37

We move all terms to the left:

4y^2+24y-(37)=0

a = 4; b = 24; c = -37;
Δ = b2-4ac
Δ = 242-4·4·(-37)
Δ = 1168
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:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{73}}{2*4}=\frac{-24-4\sqrt{73}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{73}}{2*4}=\frac{-24+4\sqrt{73}}{8}
$