6y^2-22y+15=4y-9

Solution for 6y^2-22y+15=4y-9 equation:

6y^2-22y+15=4y-9

We move all terms to the left:

6y^2-22y+15-(4y-9)=0

We get rid of parentheses

6y^2-22y-4y+9+15=0

We add all the numbers together, and all the variables

6y^2-26y+24=0

a = 6; b = -26; c = +24;
Δ = b2-4ac
Δ = -262-4·6·24
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{-(-26)-10}{2*6}=\frac{16}{12}
=1+1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+10}{2*6}=\frac{36}{12}
=3
$