6y^2-13y+12=4y^2

Solution for 6y^2-13y+12=4y^2 equation:

6y^2-13y+12=4y^2

We move all terms to the left:

6y^2-13y+12-(4y^2)=0

determiningTheFunctionDomain
6y^2-4y^2-13y+12=0

We add all the numbers together, and all the variables

2y^2-13y+12=0

a = 2; b = -13; c = +12;
Δ = b2-4ac
Δ = -132-4·2·12
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{73}}{2*2}=\frac{13-\sqrt{73}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{73}}{2*2}=\frac{13+\sqrt{73}}{4}
$