(5y+12)(9y+11)-(8y+13)(5y+12)=0

Solution for (5y+12)(9y+11)-(8y+13)(5y+12)=0 equation:

(5y+12)(9y+11)-(8y+13)(5y+12)=0

We multiply parentheses ..

(+45y^2+55y+108y+132)-(8y+13)(5y+12)=0

We get rid of parentheses

45y^2+55y+108y-(8y+13)(5y+12)+132=0

We multiply parentheses ..

45y^2-(+40y^2+96y+65y+156)+55y+108y+132=0

We add all the numbers together, and all the variables

45y^2-(+40y^2+96y+65y+156)+163y+132=0

We get rid of parentheses

45y^2-40y^2-96y-65y+163y-156+132=0

We add all the numbers together, and all the variables

5y^2+2y-24=0

a = 5; b = 2; c = -24;
Δ = b2-4ac
Δ = 22-4·5·(-24)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-22}{2*5}=\frac{-24}{10}
=-2+2/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+22}{2*5}=\frac{20}{10}
=2
$