4y^2+8y=42

Solution for 4y^2+8y=42 equation:

4y^2+8y=42

We move all terms to the left:

4y^2+8y-(42)=0

a = 4; b = 8; c = -42;
Δ = b2-4ac
Δ = 82-4·4·(-42)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{46}}{2*4}=\frac{-8-4\sqrt{46}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{46}}{2*4}=\frac{-8+4\sqrt{46}}{8}
$