8x=22/9x+5000

Solution for 8x=22/9x+5000 equation:

8x=22/9x+5000

We move all terms to the left:

8x-(22/9x+5000)=0


Domain of the equation: 9x+5000)!=0

x∈R


We get rid of parentheses

8x-22/9x-5000=0

We multiply all the terms by the denominator


8x*9x-5000*9x-22=0

Wy multiply elements

72x^2-45000x-22=0

a = 72; b = -45000; c = -22;
Δ = b2-4ac
Δ = -450002-4·72·(-22)
Δ = 2025006336
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:

$\sqrt{\Delta}=\sqrt{2025006336}=\sqrt{2304*878909}=\sqrt{2304}*\sqrt{878909}=48\sqrt{878909}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45000)-48\sqrt{878909}}{2*72}=\frac{45000-48\sqrt{878909}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45000)+48\sqrt{878909}}{2*72}=\frac{45000+48\sqrt{878909}}{144}
$