4.5-2.5x=25x^2

Solution for 4.5-2.5x=25x^2 equation:

4.5-2.5x=25x^2

We move all terms to the left:

4.5-2.5x-(25x^2)=0

determiningTheFunctionDomain
-25x^2-2.5x+4.5=0

a = -25; b = -2.5; c = +4.5;
Δ = b2-4ac
Δ = -2.52-4·(-25)·4.5
Δ = 456.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2.5)-\sqrt{456.25}}{2*-25}=\frac{2.5-\sqrt{456.25}}{-50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.5)+\sqrt{456.25}}{2*-25}=\frac{2.5+\sqrt{456.25}}{-50}
$