4y^2-12y+9=3y^2-10y+12

Solution for 4y^2-12y+9=3y^2-10y+12 equation:

4y^2-12y+9=3y^2-10y+12

We move all terms to the left:

4y^2-12y+9-(3y^2-10y+12)=0

We get rid of parentheses

4y^2-3y^2-12y+10y-12+9=0

We add all the numbers together, and all the variables

y^2-2y-3=0

a = 1; b = -2; c = -3;
Δ = b2-4ac
Δ = -22-4·1·(-3)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4}{2*1}=\frac{-2}{2}
=-1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4}{2*1}=\frac{6}{2}
=3
$