5y(y+5)=6(y-2)

Solution for 5y(y+5)=6(y-2) equation:

5y(y+5)=6(y-2)

We move all terms to the left:

5y(y+5)-(6(y-2))=0

We multiply parentheses

5y^2+25y-(6(y-2))=0


We calculate terms in parentheses: -(6(y-2)), so:

6(y-2)

We multiply parentheses

6y-12

Back to the equation:

-(6y-12)


We get rid of parentheses

5y^2+25y-6y+12=0

We add all the numbers together, and all the variables

5y^2+19y+12=0

a = 5; b = 19; c = +12;
Δ = b2-4ac
Δ = 192-4·5·12
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-11}{2*5}=\frac{-30}{10}
=-3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+11}{2*5}=\frac{-8}{10}
=-4/5
$