Y=3x^2+26x-9

Solution for Y=3x^2+26x-9 equation:

=3Y^2+26Y-9

We move all terms to the left:

-(3Y^2+26Y-9)=0

We get rid of parentheses

-3Y^2-26Y+9=0

a = -3; b = -26; c = +9;
Δ = b2-4ac
Δ = -262-4·(-3)·9
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-28}{2*-3}=\frac{-2}{-6}
=1/3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+28}{2*-3}=\frac{54}{-6}
=-9
$