(5y+15)(8y+13)-(2y+14)(5y+15)=0

Solution for (5y+15)(8y+13)-(2y+14)(5y+15)=0 equation:

(5y+15)(8y+13)-(2y+14)(5y+15)=0

We multiply parentheses ..

(+40y^2+65y+120y+195)-(2y+14)(5y+15)=0

We get rid of parentheses

40y^2+65y+120y-(2y+14)(5y+15)+195=0

We multiply parentheses ..

40y^2-(+10y^2+30y+70y+210)+65y+120y+195=0

We add all the numbers together, and all the variables

40y^2-(+10y^2+30y+70y+210)+185y+195=0

We get rid of parentheses

40y^2-10y^2-30y-70y+185y-210+195=0

We add all the numbers together, and all the variables

30y^2+85y-15=0

a = 30; b = 85; c = -15;
Δ = b2-4ac
Δ = 852-4·30·(-15)
Δ = 9025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9025}=95$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(85)-95}{2*30}=\frac{-180}{60}
=-3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(85)+95}{2*30}=\frac{10}{60}
=1/6
$