18/18.5(x-8)+10x=7x+39

Solution for 18/18.5(x-8)+10x=7x+39 equation:

18/18.5(x-8)+10x=7x+39

We move all terms to the left:

18/18.5(x-8)+10x-(7x+39)=0


Domain of the equation: 18.5(x-8)!=0

x∈R


We add all the numbers together, and all the variables

10x+18/18.5(x-8)-(7x+39)=0

We get rid of parentheses

10x+18/18.5(x-8)-7x-39=0

We multiply all the terms by the denominator


10x*18.5(x-8)-7x*18.5(x-8)-39*18.5(x-8)+18=0

Wy multiply elements

180x^2-126x^2-702x+18=0

We add all the numbers together, and all the variables

54x^2-702x+18=0

a = 54; b = -702; c = +18;
Δ = b2-4ac
Δ = -7022-4·54·18
Δ = 488916
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:

$\sqrt{\Delta}=\sqrt{488916}=\sqrt{324*1509}=\sqrt{324}*\sqrt{1509}=18\sqrt{1509}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-702)-18\sqrt{1509}}{2*54}=\frac{702-18\sqrt{1509}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-702)+18\sqrt{1509}}{2*54}=\frac{702+18\sqrt{1509}}{108}
$