45x+450=3x^2

Solution for 45x+450=3x^2 equation:

45x+450=3x^2

We move all terms to the left:

45x+450-(3x^2)=0

determiningTheFunctionDomain
-3x^2+45x+450=0

a = -3; b = 45; c = +450;
Δ = b2-4ac
Δ = 452-4·(-3)·450
Δ = 7425
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:

$\sqrt{\Delta}=\sqrt{7425}=\sqrt{225*33}=\sqrt{225}*\sqrt{33}=15\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-15\sqrt{33}}{2*-3}=\frac{-45-15\sqrt{33}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+15\sqrt{33}}{2*-3}=\frac{-45+15\sqrt{33}}{-6}
$