Y=x^2+3.25x-7.5

Solution for Y=x^2+3.25x-7.5 equation:

=Y^2+3.25Y-7.5

We move all terms to the left:

-(Y^2+3.25Y-7.5)=0

We get rid of parentheses

-Y^2-3.25Y+7.5=0

We add all the numbers together, and all the variables

-1Y^2-3.25Y+7.5=0

a = -1; b = -3.25; c = +7.5;
Δ = b2-4ac
Δ = -3.252-4·(-1)·7.5
Δ = 40.5625
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{-(-3.25)-\sqrt{40.5625}}{2*-1}=\frac{3.25-\sqrt{40.5625}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3.25)+\sqrt{40.5625}}{2*-1}=\frac{3.25+\sqrt{40.5625}}{-2}
$