Y=6x2-7x-4=0

Solution for Y=6x2-7x-4=0 equation:

=6Y^2-7Y-4=0

We move all terms to the left:

-(6Y^2-7Y-4)=0

We get rid of parentheses

-6Y^2+7Y+4=0

a = -6; b = 7; c = +4;
Δ = b2-4ac
Δ = 72-4·(-6)·4
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{145}}{2*-6}=\frac{-7-\sqrt{145}}{-12}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{145}}{2*-6}=\frac{-7+\sqrt{145}}{-12}
$