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

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



5y+34=-2y(-7y+1)
We move all terms to the left:
5y+34-(-2y(-7y+1))=0
We calculate terms in parentheses: -(-2y(-7y+1)), so:
-2y(-7y+1)
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} $

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