0.5x+8/7x=x+18

Solution for 0.5x+8/7x=x+18 equation:

0.5x+8/7x=x+18

We move all terms to the left:

0.5x+8/7x-(x+18)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

0.5x+8/7x-x-18=0

We multiply all the terms by the denominator


(0.5x)*7x-x*7x-18*7x+8=0

We add all the numbers together, and all the variables

(+0.5x)*7x-x*7x-18*7x+8=0

We multiply parentheses

0x^2-x*7x-18*7x+8=0

Wy multiply elements

0x^2-7x^2-126x+8=0

We add all the numbers together, and all the variables

-6x^2-126x+8=0

a = -6; b = -126; c = +8;
Δ = b2-4ac
Δ = -1262-4·(-6)·8
Δ = 16068
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:

$\sqrt{\Delta}=\sqrt{16068}=\sqrt{4*4017}=\sqrt{4}*\sqrt{4017}=2\sqrt{4017}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-2\sqrt{4017}}{2*-6}=\frac{126-2\sqrt{4017}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+2\sqrt{4017}}{2*-6}=\frac{126+2\sqrt{4017}}{-12}
$