x=(x+41/2)(x+9)

Solution for x=(x+41/2)(x+9) equation:

x=(x+41/2)(x+9)

We move all terms to the left:

x-((x+41/2)(x+9))=0


Domain of the equation: 2)(x+9))!=0

x∈R


We add all the numbers together, and all the variables

x-((+x+41/2)(x+9))=0

We multiply parentheses ..

-((+x^2+9x+41x^2+41/2*9))+x=0

We multiply all the terms by the denominator


-((+x^2+9x+41x^2+41+x*2*9))=0


We calculate terms in parentheses: -((+x^2+9x+41x^2+41+x*2*9)), so:

(+x^2+9x+41x^2+41+x*2*9)

We get rid of parentheses

x^2+41x^2+9x+x*2*9+41

We add all the numbers together, and all the variables

42x^2+9x+x*2*9+41

Wy multiply elements

42x^2+9x+18x*9+41

Wy multiply elements

42x^2+9x+162x+41

We add all the numbers together, and all the variables

42x^2+171x+41

Back to the equation:

-(42x^2+171x+41)


We get rid of parentheses

-42x^2-171x-41=0

a = -42; b = -171; c = -41;
Δ = b2-4ac
Δ = -1712-4·(-42)·(-41)
Δ = 22353
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-171)-\sqrt{22353}}{2*-42}=\frac{171-\sqrt{22353}}{-84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-171)+\sqrt{22353}}{2*-42}=\frac{171+\sqrt{22353}}{-84}
$