2y(4y+7)=49

Solution for 2y(4y+7)=49 equation:

2y(4y+7)=49

We move all terms to the left:

2y(4y+7)-(49)=0

We multiply parentheses

8y^2+14y-49=0

a = 8; b = 14; c = -49;
Δ = b2-4ac
Δ = 142-4·8·(-49)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-42}{2*8}=\frac{-56}{16}
=-3+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+42}{2*8}=\frac{28}{16}
=1+3/4
$