Y=2x^2+7x-12

Solution for Y=2x^2+7x-12 equation:

=2Y^2+7Y-12

We move all terms to the left:

-(2Y^2+7Y-12)=0

We get rid of parentheses

-2Y^2-7Y+12=0

a = -2; b = -7; c = +12;
Δ = b2-4ac
Δ = -72-4·(-2)·12
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*-2}=\frac{7-\sqrt{145}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{145}}{2*-2}=\frac{7+\sqrt{145}}{-4}
$