1350=x*(x+45)

Solution for 1350=x*(x+45) equation:

1350=x(x+45)

We move all terms to the left:

1350-(x(x+45))=0


We calculate terms in parentheses: -(x(x+45)), so:

x(x+45)

We multiply parentheses

x^2+45x

Back to the equation:

-(x^2+45x)


We get rid of parentheses

-x^2-45x+1350=0

We add all the numbers together, and all the variables

-1x^2-45x+1350=0

a = -1; b = -45; c = +1350;
Δ = b2-4ac
Δ = -452-4·(-1)·1350
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*-1}=\frac{45-15\sqrt{33}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+15\sqrt{33}}{2*-1}=\frac{45+15\sqrt{33}}{-2}
$