x(x+3)=45-x

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

x(x+3)=45-x

We move all terms to the left:

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

We add all the numbers together, and all the variables

x(x+3)-(-1x+45)=0

We multiply parentheses

x^2+3x-(-1x+45)=0

We get rid of parentheses

x^2+3x+1x-45=0

We add all the numbers together, and all the variables

x^2+4x-45=0

a = 1; b = 4; c = -45;
Δ = b2-4ac
Δ = 42-4·1·(-45)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-14}{2*1}=\frac{-18}{2}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+14}{2*1}=\frac{10}{2}
=5
$