2y^2-14y+49=42

Solution for 2y^2-14y+49=42 equation:

2y^2-14y+49=42

We move all terms to the left:

2y^2-14y+49-(42)=0

We add all the numbers together, and all the variables

2y^2-14y+7=0

a = 2; b = -14; c = +7;
Δ = b2-4ac
Δ = -142-4·2·7
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{35}}{2*2}=\frac{14-2\sqrt{35}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{35}}{2*2}=\frac{14+2\sqrt{35}}{4}
$