45=15x+2.25x^2

Solution for 45=15x+2.25x^2 equation:

45=15x+2.25x^2

We move all terms to the left:

45-(15x+2.25x^2)=0

We get rid of parentheses

-2.25x^2-15x+45=0

a = -2.25; b = -15; c = +45;
Δ = b2-4ac
Δ = -152-4·(-2.25)·45
Δ = 630
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{630}=\sqrt{9*70}=\sqrt{9}*\sqrt{70}=3\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{70}}{2*-2.25}=\frac{15-3\sqrt{70}}{-4.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{70}}{2*-2.25}=\frac{15+3\sqrt{70}}{-4.5}
$