(2y+5)(7y+12)+(13y+9)(2y+5)=0

Solution for (2y+5)(7y+12)+(13y+9)(2y+5)=0 equation:

(2y+5)(7y+12)+(13y+9)(2y+5)=0

We multiply parentheses ..

(+14y^2+24y+35y+60)+(13y+9)(2y+5)=0

We get rid of parentheses

14y^2+24y+35y+(13y+9)(2y+5)+60=0

We multiply parentheses ..

14y^2+(+26y^2+65y+18y+45)+24y+35y+60=0

We add all the numbers together, and all the variables

14y^2+(+26y^2+65y+18y+45)+59y+60=0

We get rid of parentheses

14y^2+26y^2+65y+18y+59y+45+60=0

We add all the numbers together, and all the variables

40y^2+142y+105=0

a = 40; b = 142; c = +105;
Δ = b2-4ac
Δ = 1422-4·40·105
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(142)-58}{2*40}=\frac{-200}{80}
=-2+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(142)+58}{2*40}=\frac{-84}{80}
=-1+1/20
$