Y=6t^2-10t

Solution for Y=6t^2-10t equation:

=6Y^2-10Y

We move all terms to the left:

-(6Y^2-10Y)=0

We get rid of parentheses

-6Y^2+10Y=0

a = -6; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-6)·0
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{-(10)-10}{2*-6}=\frac{-20}{-12}
=1+2/3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-6}=\frac{0}{-12}
=0
$