(12y^2+17y-4)+(9y^2-13y+3)=0

Solution for (12y^2+17y-4)+(9y^2-13y+3)=0 equation:

(12y^2+17y-4)+(9y^2-13y+3)=0

We get rid of parentheses

12y^2+9y^2+17y-13y-4+3=0

We add all the numbers together, and all the variables

21y^2+4y-1=0

a = 21; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·21·(-1)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-10}{2*21}=\frac{-14}{42}
=-1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+10}{2*21}=\frac{6}{42}
=1/7
$