3x^2-90*x=-450

Solution for 3x^2-90*x=-450 equation:

3x^2-90x=-450

We move all terms to the left:

3x^2-90x-(-450)=0

We add all the numbers together, and all the variables

3x^2-90x+450=0

a = 3; b = -90; c = +450;
Δ = b2-4ac
Δ = -902-4·3·450
Δ = 2700
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:

$\sqrt{\Delta}=\sqrt{2700}=\sqrt{900*3}=\sqrt{900}*\sqrt{3}=30\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-30\sqrt{3}}{2*3}=\frac{90-30\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+30\sqrt{3}}{2*3}=\frac{90+30\sqrt{3}}{6}
$