Y=6X2+5x-4

Solution for Y=6X2+5x-4 equation:

=6Y^2+5Y-4

We move all terms to the left:

-(6Y^2+5Y-4)=0

We get rid of parentheses

-6Y^2-5Y+4=0

a = -6; b = -5; c = +4;
Δ = b2-4ac
Δ = -52-4·(-6)·4
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-11}{2*-6}=\frac{-6}{-12}
=1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+11}{2*-6}=\frac{16}{-12}
=-1+1/3
$