Y=2x^2+24x-25

Solution for Y=2x^2+24x-25 equation:

=2Y^2+24Y-25

We move all terms to the left:

-(2Y^2+24Y-25)=0

We get rid of parentheses

-2Y^2-24Y+25=0

a = -2; b = -24; c = +25;
Δ = b2-4ac
Δ = -242-4·(-2)·25
Δ = 776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{776}=\sqrt{4*194}=\sqrt{4}*\sqrt{194}=2\sqrt{194}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{194}}{2*-2}=\frac{24-2\sqrt{194}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{194}}{2*-2}=\frac{24+2\sqrt{194}}{-4}
$