Y-15=2x^2-13x

Solution for Y-15=2x^2-13x equation:

-15=2Y^2-13Y

We move all terms to the left:

-15-(2Y^2-13Y)=0

We get rid of parentheses

-2Y^2+13Y-15=0

a = -2; b = 13; c = -15;
Δ = b2-4ac
Δ = 132-4·(-2)·(-15)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-7}{2*-2}=\frac{-20}{-4}
=+5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+7}{2*-2}=\frac{-6}{-4}
=1+1/2
$