5y^2+2y^2-10y-12y+3=0

Solution for 5y^2+2y^2-10y-12y+3=0 equation:

5y^2+2y^2-10y-12y+3=0

We add all the numbers together, and all the variables

7y^2-22y+3=0

a = 7; b = -22; c = +3;
Δ = b2-4ac
Δ = -222-4·7·3
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-20}{2*7}=\frac{2}{14}
=1/7
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+20}{2*7}=\frac{42}{14}
=3
$