(5y+4)(y+6)=-5(5y+4)

Solution for (5y+4)(y+6)=-5(5y+4) equation:

(5y+4)(y+6)=-5(5y+4)

We move all terms to the left:

(5y+4)(y+6)-(-5(5y+4))=0

We multiply parentheses ..

(+5y^2+30y+4y+24)-(-5(5y+4))=0


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

-5(5y+4)

We multiply parentheses

-25y-20

Back to the equation:

-(-25y-20)


We get rid of parentheses

5y^2+30y+4y+25y+24+20=0

We add all the numbers together, and all the variables

5y^2+59y+44=0

a = 5; b = 59; c = +44;
Δ = b2-4ac
Δ = 592-4·5·44
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(59)-51}{2*5}=\frac{-110}{10}
=-11
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(59)+51}{2*5}=\frac{-8}{10}
=-4/5
$