-5/8x=x+9

Solution for -5/8x=x+9 equation:

-5/8x=x+9

We move all terms to the left:

-5/8x-(x+9)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

-5/8x-x-9=0

We multiply all the terms by the denominator


-x*8x-9*8x-5=0

Wy multiply elements

-8x^2-72x-5=0

a = -8; b = -72; c = -5;
Δ = b2-4ac
Δ = -722-4·(-8)·(-5)
Δ = 5024
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:

$\sqrt{\Delta}=\sqrt{5024}=\sqrt{16*314}=\sqrt{16}*\sqrt{314}=4\sqrt{314}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{314}}{2*-8}=\frac{72-4\sqrt{314}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{314}}{2*-8}=\frac{72+4\sqrt{314}}{-16}
$