0.5+8/7x=x+36

Solution for 0.5+8/7x=x+36 equation:

0.5+8/7x=x+36

We move all terms to the left:

0.5+8/7x-(x+36)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

8/7x-x-36+0.5=0

We multiply all the terms by the denominator


-x*7x-36*7x+(0.5)*7x+8=0

We multiply parentheses

-x*7x-36*7x+3.5x+8=0

Wy multiply elements

-7x^2-252x+3.5x+8=0

We add all the numbers together, and all the variables

-7x^2-248.5x+8=0

a = -7; b = -248.5; c = +8;
Δ = b2-4ac
Δ = -248.52-4·(-7)·8
Δ = 61976.25
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{-(-248.5)-\sqrt{61976.25}}{2*-7}=\frac{248.5-\sqrt{61976.25}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-248.5)+\sqrt{61976.25}}{2*-7}=\frac{248.5+\sqrt{61976.25}}{-14}
$