90=45x-3x^2

Solution for 90=45x-3x^2 equation:

90=45x-3x^2

We move all terms to the left:

90-(45x-3x^2)=0

We get rid of parentheses

3x^2-45x+90=0

a = 3; b = -45; c = +90;
Δ = b2-4ac
Δ = -452-4·3·90
Δ = 945
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:

$\sqrt{\Delta}=\sqrt{945}=\sqrt{9*105}=\sqrt{9}*\sqrt{105}=3\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{105}}{2*3}=\frac{45-3\sqrt{105}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{105}}{2*3}=\frac{45+3\sqrt{105}}{6}
$