(2y+13)(5y+8)=0

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

(2y+13)(5y+8)=0

We multiply parentheses ..

(+10y^2+16y+65y+104)=0

We get rid of parentheses

10y^2+16y+65y+104=0

We add all the numbers together, and all the variables

10y^2+81y+104=0

a = 10; b = 81; c = +104;
Δ = b2-4ac
Δ = 812-4·10·104
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-49}{2*10}=\frac{-130}{20}
=-6+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+49}{2*10}=\frac{-32}{20}
=-1+3/5
$