Y=2x^2-25x+75

Solution for Y=2x^2-25x+75 equation:

=2Y^2-25Y+75

We move all terms to the left:

-(2Y^2-25Y+75)=0

We get rid of parentheses

-2Y^2+25Y-75=0

a = -2; b = 25; c = -75;
Δ = b2-4ac
Δ = 252-4·(-2)·(-75)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-5}{2*-2}=\frac{-30}{-4}
=7+1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+5}{2*-2}=\frac{-20}{-4}
=+5
$