Y=6x^2-29x+35

Solution for Y=6x^2-29x+35 equation:

=6Y^2-29Y+35

We move all terms to the left:

-(6Y^2-29Y+35)=0

We get rid of parentheses

-6Y^2+29Y-35=0

a = -6; b = 29; c = -35;
Δ = b2-4ac
Δ = 292-4·(-6)·(-35)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-1}{2*-6}=\frac{-30}{-12}
=2+1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+1}{2*-6}=\frac{-28}{-12}
=2+1/3
$