(1/2)x+(8/7)x=x+18

Solution for (1/2)x+(8/7)x=x+18 equation:

(1/2)x+(8/7)x=x+18

We move all terms to the left:

(1/2)x+(8/7)x-(x+18)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 7)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)x+(+8/7)x-(x+18)=0

We multiply parentheses

x^2+8x^2-(x+18)=0

We get rid of parentheses

x^2+8x^2-x-18=0

We add all the numbers together, and all the variables

9x^2-1x-18=0

a = 9; b = -1; c = -18;
Δ = b2-4ac
Δ = -12-4·9·(-18)
Δ = 649
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{-(-1)-\sqrt{649}}{2*9}=\frac{1-\sqrt{649}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{649}}{2*9}=\frac{1+\sqrt{649}}{18}
$