Y=2x^2+11x-13

Solution for Y=2x^2+11x-13 equation:

=2Y^2+11Y-13

We move all terms to the left:

-(2Y^2+11Y-13)=0

We get rid of parentheses

-2Y^2-11Y+13=0

a = -2; b = -11; c = +13;
Δ = b2-4ac
Δ = -112-4·(-2)·13
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-15}{2*-2}=\frac{-4}{-4}
=1
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+15}{2*-2}=\frac{26}{-4}
=-6+1/2
$