(6y+5)(5y+17)=0

Solution for (6y+5)(5y+17)=0 equation:

(6y+5)(5y+17)=0

We multiply parentheses ..

(+30y^2+102y+25y+85)=0

We get rid of parentheses

30y^2+102y+25y+85=0

We add all the numbers together, and all the variables

30y^2+127y+85=0

a = 30; b = 127; c = +85;
Δ = b2-4ac
Δ = 1272-4·30·85
Δ = 5929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5929}=77$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(127)-77}{2*30}=\frac{-204}{60}
=-3+2/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(127)+77}{2*30}=\frac{-50}{60}
=-5/6
$