(Y+5)(y+2)=(y+1)(y-3)

Solution for (Y+5)(y+2)=(y+1)(y-3) equation:

(+5)(Y+2)=(Y+1)(Y-3)

We move all terms to the left:

(+5)(Y+2)-((Y+1)(Y-3))=0

We add all the numbers together, and all the variables

5(Y+2)-((Y+1)(Y-3))=0

We multiply parentheses

5Y-((Y+1)(Y-3))+10=0

We multiply parentheses ..

-((+Y^2-3Y+Y-3))+5Y+10=0


We calculate terms in parentheses: -((+Y^2-3Y+Y-3)), so:

(+Y^2-3Y+Y-3)

We get rid of parentheses

Y^2-3Y+Y-3

We add all the numbers together, and all the variables

Y^2-2Y-3

Back to the equation:

-(Y^2-2Y-3)


We add all the numbers together, and all the variables

5Y-(Y^2-2Y-3)+10=0

We get rid of parentheses

-Y^2+5Y+2Y+3+10=0

We add all the numbers together, and all the variables

-1Y^2+7Y+13=0

a = -1; b = 7; c = +13;
Δ = b2-4ac
Δ = 72-4·(-1)·13
Δ = 101
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{101}}{2*-1}=\frac{-7-\sqrt{101}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{101}}{2*-1}=\frac{-7+\sqrt{101}}{-2}
$