x(x+18)=x/2+39

Solution for x(x+18)=x/2+39 equation:

x(x+18)=x/2+39

We move all terms to the left:

x(x+18)-(x/2+39)=0

We multiply parentheses

x^2+18x-(x/2+39)=0

We get rid of parentheses

x^2+18x-x/2-39=0

We multiply all the terms by the denominator


x^2*2+18x*2-x-39*2=0

We add all the numbers together, and all the variables

x^2*2-1x+18x*2-78=0

Wy multiply elements

2x^2-1x+36x-78=0

We add all the numbers together, and all the variables

2x^2+35x-78=0

a = 2; b = 35; c = -78;
Δ = b2-4ac
Δ = 352-4·2·(-78)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-43}{2*2}=\frac{-78}{4}
=-19+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+43}{2*2}=\frac{8}{4}
=2
$