0.5+8/7x=x+27

Solution for 0.5+8/7x=x+27 equation:

0.5+8/7x=x+27

We move all terms to the left:

0.5+8/7x-(x+27)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

8/7x-x-27+0.5=0

We multiply all the terms by the denominator


-x*7x-27*7x+(0.5)*7x+8=0

We multiply parentheses

-x*7x-27*7x+3.5x+8=0

Wy multiply elements

-7x^2-189x+3.5x+8=0

We add all the numbers together, and all the variables

-7x^2-185.5x+8=0

a = -7; b = -185.5; c = +8;
Δ = b2-4ac
Δ = -185.52-4·(-7)·8
Δ = 34634.25
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{-(-185.5)-\sqrt{34634.25}}{2*-7}=\frac{185.5-\sqrt{34634.25}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-185.5)+\sqrt{34634.25}}{2*-7}=\frac{185.5+\sqrt{34634.25}}{-14}
$