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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(5(4y-2)y), so:

5(4y-2)y

We multiply parentheses

20y^2-10y

Back to the equation:

-(20y^2-10y)


We get rid of parentheses

-20y^2+y+10y+9=0

We add all the numbers together, and all the variables

-20y^2+11y+9=0

a = -20; b = 11; c = +9;
Δ = b2-4ac
Δ = 112-4·(-20)·9
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-29}{2*-20}=\frac{-40}{-40}
=1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+29}{2*-20}=\frac{18}{-40}
=-9/20
$