(x-3)(x+45)=600

Solution for (x-3)(x+45)=600 equation:

(x-3)(x+45)=600

We move all terms to the left:

(x-3)(x+45)-(600)=0

We multiply parentheses ..

(+x^2+45x-3x-135)-600=0

We get rid of parentheses

x^2+45x-3x-135-600=0

We add all the numbers together, and all the variables

x^2+42x-735=0

a = 1; b = 42; c = -735;
Δ = b2-4ac
Δ = 422-4·1·(-735)
Δ = 4704
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:

$\sqrt{\Delta}=\sqrt{4704}=\sqrt{784*6}=\sqrt{784}*\sqrt{6}=28\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-28\sqrt{6}}{2*1}=\frac{-42-28\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+28\sqrt{6}}{2*1}=\frac{-42+28\sqrt{6}}{2}
$