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

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

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

We move all terms to the left:

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


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

(y+1)

We get rid of parentheses

y+1

Back to the equation:

-(y+1)


We get rid of parentheses

5y^2-4y-y-1-9=0

We add all the numbers together, and all the variables

5y^2-5y-10=0

a = 5; b = -5; c = -10;
Δ = b2-4ac
Δ = -52-4·5·(-10)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-15}{2*5}=\frac{-10}{10}
=-1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+15}{2*5}=\frac{20}{10}
=2
$