(6y-1)(y+5)=15y-9

Solution for (6y-1)(y+5)=15y-9 equation:

(6y-1)(y+5)=15y-9

We move all terms to the left:

(6y-1)(y+5)-(15y-9)=0

We get rid of parentheses

(6y-1)(y+5)-15y+9=0

We multiply parentheses ..

(+6y^2+30y-1y-5)-15y+9=0

We get rid of parentheses

6y^2+30y-1y-15y-5+9=0

We add all the numbers together, and all the variables

6y^2+14y+4=0

a = 6; b = 14; c = +4;
Δ = b2-4ac
Δ = 142-4·6·4
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-10}{2*6}=\frac{-24}{12}
=-2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10}{2*6}=\frac{-4}{12}
=-1/3
$