45=(x+4)x

Solution for 45=(x+4)x equation:

45=(x+4)x

We move all terms to the left:

45-((x+4)x)=0


We calculate terms in parentheses: -((x+4)x), so:

(x+4)x

We multiply parentheses

x^2+4x

Back to the equation:

-(x^2+4x)


We get rid of parentheses

-x^2-4x+45=0

We add all the numbers together, and all the variables

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