0.5x+(8/7x)=x+9

Solution for 0.5x+(8/7x)=x+9 equation:

0.5x+(8/7x)=x+9

We move all terms to the left:

0.5x+(8/7x)-(x+9)=0


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

0.5x+(+8/7x)-(x+9)=0

We get rid of parentheses

0.5x+8/7x-x-9=0

We multiply all the terms by the denominator


(0.5x)*7x-x*7x-9*7x+8=0

We add all the numbers together, and all the variables

(+0.5x)*7x-x*7x-9*7x+8=0

We multiply parentheses

0x^2-x*7x-9*7x+8=0

Wy multiply elements

0x^2-7x^2-63x+8=0

We add all the numbers together, and all the variables

-6x^2-63x+8=0

a = -6; b = -63; c = +8;
Δ = b2-4ac
Δ = -632-4·(-6)·8
Δ = 4161
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{-(-63)-\sqrt{4161}}{2*-6}=\frac{63-\sqrt{4161}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+\sqrt{4161}}{2*-6}=\frac{63+\sqrt{4161}}{-12}
$