Y=45x2+630x-235

Solution for Y=45x2+630x-235 equation:

=45Y^2+630Y-235

We move all terms to the left:

-(45Y^2+630Y-235)=0

We get rid of parentheses

-45Y^2-630Y+235=0

a = -45; b = -630; c = +235;
Δ = b2-4ac
Δ = -6302-4·(-45)·235
Δ = 439200
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:

$\sqrt{\Delta}=\sqrt{439200}=\sqrt{3600*122}=\sqrt{3600}*\sqrt{122}=60\sqrt{122}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-630)-60\sqrt{122}}{2*-45}=\frac{630-60\sqrt{122}}{-90}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-630)+60\sqrt{122}}{2*-45}=\frac{630+60\sqrt{122}}{-90}
$