Y=2x2+7x-4

Solution for Y=2x2+7x-4 equation:

=2Y^2+7Y-4

We move all terms to the left:

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

We get rid of parentheses

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

a = -2; b = -7; c = +4;
Δ = b2-4ac
Δ = -72-4·(-2)·4
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-9}{2*-2}=\frac{-2}{-4}
=1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+9}{2*-2}=\frac{16}{-4}
=-4
$