(5y+7)(5y+7)=2

Solution for (5y+7)(5y+7)=2 equation:

(5y+7)(5y+7)=2

We move all terms to the left:

(5y+7)(5y+7)-(2)=0

We multiply parentheses ..

(+25y^2+35y+35y+49)-2=0

We get rid of parentheses

25y^2+35y+35y+49-2=0

We add all the numbers together, and all the variables

25y^2+70y+47=0

a = 25; b = 70; c = +47;
Δ = b2-4ac
Δ = 702-4·25·47
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-10\sqrt{2}}{2*25}=\frac{-70-10\sqrt{2}}{50}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+10\sqrt{2}}{2*25}=\frac{-70+10\sqrt{2}}{50}
$