30x^2+450x=-1350

Solution for 30x^2+450x=-1350 equation:

30x^2+450x=-1350

We move all terms to the left:

30x^2+450x-(-1350)=0

We add all the numbers together, and all the variables

30x^2+450x+1350=0

a = 30; b = 450; c = +1350;
Δ = b2-4ac
Δ = 4502-4·30·1350
Δ = 40500
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:

$\sqrt{\Delta}=\sqrt{40500}=\sqrt{8100*5}=\sqrt{8100}*\sqrt{5}=90\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(450)-90\sqrt{5}}{2*30}=\frac{-450-90\sqrt{5}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(450)+90\sqrt{5}}{2*30}=\frac{-450+90\sqrt{5}}{60}
$