x-45=3x(x+25)

Solution for x-45=3x(x+25) equation:

x-45=3x(x+25)

We move all terms to the left:

x-45-(3x(x+25))=0


We calculate terms in parentheses: -(3x(x+25)), so:

3x(x+25)

We multiply parentheses

3x^2+75x

Back to the equation:

-(3x^2+75x)


We get rid of parentheses

-3x^2+x-75x-45=0

We add all the numbers together, and all the variables

-3x^2-74x-45=0

a = -3; b = -74; c = -45;
Δ = b2-4ac
Δ = -742-4·(-3)·(-45)
Δ = 4936
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:

$\sqrt{\Delta}=\sqrt{4936}=\sqrt{4*1234}=\sqrt{4}*\sqrt{1234}=2\sqrt{1234}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-2\sqrt{1234}}{2*-3}=\frac{74-2\sqrt{1234}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+2\sqrt{1234}}{2*-3}=\frac{74+2\sqrt{1234}}{-6}
$