5y+34=-2(-7y+1)y=

Solution for 5y+34=-2(-7y+1)y= equation:

5y+34=-2(-7y+1)y=

We move all terms to the left:

5y+34-(-2(-7y+1)y)=0


We calculate terms in parentheses: -(-2(-7y+1)y), so:

-2(-7y+1)y

We multiply parentheses

14y^2-2y

Back to the equation:

-(14y^2-2y)


We get rid of parentheses

-14y^2+5y+2y+34=0

We add all the numbers together, and all the variables

-14y^2+7y+34=0

a = -14; b = 7; c = +34;
Δ = b2-4ac
Δ = 72-4·(-14)·34
Δ = 1953
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:

$\sqrt{\Delta}=\sqrt{1953}=\sqrt{9*217}=\sqrt{9}*\sqrt{217}=3\sqrt{217}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3\sqrt{217}}{2*-14}=\frac{-7-3\sqrt{217}}{-28}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3\sqrt{217}}{2*-14}=\frac{-7+3\sqrt{217}}{-28}
$