Y+6=10x^2-11x

Solution for Y+6=10x^2-11x equation:

+6=10Y^2-11Y

We move all terms to the left:

+6-(10Y^2-11Y)=0

We get rid of parentheses

-10Y^2+11Y+6=0

a = -10; b = 11; c = +6;
Δ = b2-4ac
Δ = 112-4·(-10)·6
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-19}{2*-10}=\frac{-30}{-20}
=1+1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+19}{2*-10}=\frac{8}{-20}
=-2/5
$