(5y+1)2-4(y-1)2=(y+5)(9y+5)

Solution for (5y+1)2-4(y-1)2=(y+5)(9y+5) equation:

(5y+1)2-4(y-1)2=(y+5)(9y+5)

We move all terms to the left:

(5y+1)2-4(y-1)2-((y+5)(9y+5))=0

We multiply parentheses

10y-8y-((y+5)(9y+5))+2+8=0

We multiply parentheses ..

-((+9y^2+5y+45y+25))+10y-8y+2+8=0


We calculate terms in parentheses: -((+9y^2+5y+45y+25)), so:

(+9y^2+5y+45y+25)

We get rid of parentheses

9y^2+5y+45y+25

We add all the numbers together, and all the variables

9y^2+50y+25

Back to the equation:

-(9y^2+50y+25)


We add all the numbers together, and all the variables

2y-(9y^2+50y+25)+10=0

We get rid of parentheses

-9y^2+2y-50y-25+10=0

We add all the numbers together, and all the variables

-9y^2-48y-15=0

a = -9; b = -48; c = -15;
Δ = b2-4ac
Δ = -482-4·(-9)·(-15)
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{-(-48)-42}{2*-9}=\frac{6}{-18}
=-1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+42}{2*-9}=\frac{90}{-18}
=-5
$